Geometry Term I

Geometry Ch 1
http://MCSMGeometry.weebly.com
Lesson 1—What are the three undefined terms in Geometry? (Section 1.1)
HW #1: P5 – 8: 1, 5, 6, 8, 15, 19, 33, 35, 36
Objectives: name a segment, a line, a ray, a plane
know the terms collinear, parallel, skew and coplanar
know the intersection of planes and lines
Lesson 2—Aim: How do we prove two line segments are congruent? (Section 1.2)
HW #2: P12 – 14: 1, 13 – 14, 21 – 26, 28, 29.
Objectives: know the segment addition postulate
Know the difference between congruent and equal
Lesson 3&4—Aim: How do we find the midpoint when given two points? (Section 1.3)
HW #3-4: P19 – 20: 4, 5, 11, 13, 17 – 19, 25 – 27, 47
Objectives: know the midpoint divides a segment into two equal pieces
Know how to find the coordinates of the midpoint when given two endpoints
Know how to find the coordinates of an endpoint when given an endpoint and
the midpoint.
Lesson 5—Aim: How do we find the distance between two points? (Section 1.3) 2 Days
HW #5: P20 – 22: 20, 23, 30 – 32, 41, 44, 45.
Objectives: know that distance between two points is the same as the hypotenuse of a right
triangle.
know how to express the length or distance in simplest radical form or decimals
know how to find the perimeter of a triangle when given the three vertices.
Lesson 6—Aim: How do we classify angles? (Section 1.4)
HW #6: P28 – 30: 3 – 5, 11 – 14, 21 – 23, 25 – 27, 41 – 42.
Objectives: know how to name an angle
Know the different types of angles: acute, right, obtuse and straight
Know the angle addition postulate
Know that linear pairs are supplementary
Lesson 7—Aim: How do we describe angle pair relationships? (Section 1.5)
HW #7: P38 – 39: 3 – 7, 17, 19, 31, 32, 45*
Objectives: know the terms adjacent
Know the complementary angles add up to 90 degrees and supplementary angles add
up to 180 degrees.
Lesson 8—Aim: How do we classify polygons? (Sections 1.6-1.7)
HW #8: P44 – 46: 1, 3 – 6, 8 – 13, 15 – 17, 28, 30
Objectives: know what is a triangle, quadrilateral, pentagon or hexagon
Know what is a convex or concave polygon
Know the terms equiangular, equilateral and regular
Ch 1 Review/Uniform Unit Test
Common Core Standards Addressed
G-CO.1
Know precise definitions of angle, circle, perpendicular line, parallel line, and line
segment, based on the undefined notions of point, line, distance along a line, and
distance around a circular arc.
G-CO.2
Represent transformations in the plane using, e.g., transparencies and geometry
software; describe transformations as functions that take points in the plane as inputs
and give other points as outputs. Compare transformations that preserve distance and
angle to those that do not (e.g., translation versus horizontal stretch).
G-CO.5
Given a geometric figure and a rotation, reflection, or translation, draw the transformed
figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence
of transformations that will carry a given figure onto another.
G-CO.6
Use geometric descriptions of rigid motions to transform figures and to predict the
effect of a given rigid motion on a given figure; given two figures, use the definition of
congruence in terms of rigid motions to decide if they are congruent.
G-CO.9
Prove theorems about lines and angles. Theorems include: vertical angles are
congruent; when a transversal crosses parallel lines, alternate interior angles are
congruent and corresponding angles are congruent; points on a perpendicular bisector
of a line segment are exactly those equidistant from the segment’s endpoints.
G-PFE.4
Use coordinates to prove simple geometric theorems algebraically. For example, prove
or disprove that a figure defined by four given points in the coordinate plane is a
rectangle; prove or disprove that the point (1, -3) lies on the circle centered at the
origin and containing the point (0, 2).
G-PFE.6
Find the point on a directed line segment between two given points that partitions the
segment in a given ratio.
A-CED.1
Create equations in one variable and use them to solve problem.
A-CED.4
Rearrange formulas to highlight a quantity of interest, using the same reasoning as
solving equations.
Methods of Differentiated Instructions
Revolution K-12, a student-driven online learning platform, is used to differentiate instruction for all
students in class and subject areas.
All students are held to the Common Core-aligned standards. Teacher performs formative assessments
through lessons to check student understanding, including cold-calling, student board work, and exit
tickets. Teacher circulates room to perform further formative assessments and to guide small groups and
individuals.
Lower-performing students are grouped heterogeneously with higher-performing students using
assessment data, interests, and work habits, to encourage student-to-student engagement and learning.
They are also provided guided notes and graphic organizers to build schemas.
English Language Learners are paired with students who are fluent in English, and given extra time.
Vocabulary is pronounced several times and accompanied by alternative words or phrases that are
simplified. Visual aids, including pictures, Smart boards, and manipulatives, help students make clear
connections to the text.
Students with Special Needs are grouped with helpers and given instructions or assessments with
simplified language or extra time. Color-coding on the Smart board help illustrate steps required to solve
a problem. Hands-on activities are provided to help construct student learning.
Gifted/Honor students are given challenge problems during lessons, homework, and summative
assessments, which earn extra credits. They are expected to complete the whole worksheet, and are
given challenge (e.g. open-ended) problems that develop higher-level thinking.
Geometry Ch 2
http://PassGeometry.weebly.com
Lesson 10—Aim: How do we use inductive reasoning and deductive reasoning? (Section 2.1/2.2) 2
Days
HW #10: P75: 5 – 7, 11, 13 – 14, 17, 20, 22.
Objectives: Know what inductive reasoning, conjecture, and counterexample are
Know how to use inductive reasoning to form conjectures
Know how to find a counterexample to disapprove a conjecture
Know what deductive reasoning is
Lesson 11—Aim: How do we evaluate the truth value of a conjunction or disjunction?
HW #11: Worksheet
Objectives: know what is a conjunction and a disjunction
Know when a conjunction is true and when a disjunction is true
Lesson 12—Aim: How do we analyze conditional statements? (Section 2.2)
HW #12: P83 – 84: 9 – 10, 12, 13, 19, 21, 26.
*find a news article that contains any of the statements we learned in class
Objectives: know how to write a conditional statement and its converse, inverse and
Contrapositive
Know how to write the negation of a statement and determine its truth value
Know the term logically equivalent and that the contrapositive is always logically
equivalent to the conditional statement.
Lesson 13—Aim: How do we use deductive reasoning? (Section 2.2)
HW #13: p90-91: 1, 4 –12, 15
Objective: Know what deductive reasoning is
Know or be able to apply the Laws of Syllogism and Detachment
Lesson 14&15—Aim: How do we use postulates and diagrams? (Section 2.4)
HW #14&15: P99 -100: 3 – 5, 14 – 23.
Objectives: Know, when given a diagram, what to assume and what not to assume
Know how to answer questions about planes and lines.
Know the symbol for perpendicular
Lesson 16—Aim: How do we prove statements about segments and angles? (Section 2.6)
HW #16: P116 – 118: 1, 5 – 11, 17
Objectives: know the reflexive property, symmetric property and the transitive property.
Know how to write a short two-column proof
Lesson 17—Aim: What are the angle pair relationships? (Section 2.7)
HW #17: P127-129: 4 – 5, 12, 28, 31 – 34.
Objectives: know the congruent complements theorem and the congruent supplements theorem
Lesson 18—Aim: What are the angle pair relationships? (Section 2.7)
HW #18: P128: 17 – 21.
Objectives: know the vertical angles congruence theorem and the linear pair postulate
Ch 2 Review/Uniform Unit Test
Common Core Standards Addressed
G-CO.9
Prove theorems about lines and angles. Theorems include: vertical angles are congruent;
when a transversal crosses parallel lines, alternate interior angles are congruent and
corresponding angles are congruent; points on a perpendicular bisector of a line segment
are exactly those equidistant from the segment’s endpoints.
G-CO.12 Make formal geometric constructions with a variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
Copying a segment; copying an angle; bisecting a segment; bisecting an angle;
constructing perpendicular lines, including the perpendicular bisector of a line segment;
and constructing a line parallel to a given line through a point not on the line.
Methods of Differentiated Instructions
Revolution K-12, a student-driven online learning platform, is used to differentiate instruction for all
students in class and subject areas.
All students are held to the Common Core-aligned standards. Teacher performs formative assessments
through lessons to check student understanding, including cold-calling, student board work, and exit
tickets. Teacher circulates room to perform further formative assessments and to guide small groups and
individuals.
Lower-performing students are grouped heterogeneously with higher-performing students using
assessment data, interests, and work habits, to encourage student-to-student engagement and learning.
They are also provided guided notes and graphic organizers to build schemas.
English Language Learners are paired with students who are fluent in English, and given extra time.
Vocabulary is pronounced several times and accompanied by alternative words or phrases that are
simplified. Visual aids, including pictures, Smart boards, and manipulatives, help students make clear
connections to the text.
Students with Special Needs are grouped with helpers and given instructions or assessments with
simplified language or extra time. Color-coding on the Smart board help illustrate steps required to solve
a problem. Hands-on activities are provided to help construct student learning.
Gifted/Honor students are given challenge problems during lessons, homework, and summative
assessments, which earn extra credits. They are expected to complete the whole worksheet, and are
given challenge (e.g. open-ended) problems that develop higher-level thinking.
Geometry Ch 3
Class website: http://PassGeometry.weebly.com
For graph paper, ask Mr. Lee after class, or visit
http://mathbits.com/MathBits/StudentResources/GraphPaper/GraphPaper.htm
To receive credit, you must copy the questions and all diagrams, and use a straightedge for lines.
(Long word problems may be paraphrased, i.e. summarized.)
Some homework will be distributed in class as handouts, with some differences in assigned problems.
Lesson 20 – Aim: What are the properties of parallel lines cut by a transversal? (Section 3.2)
2 Days
HW #20: P157 – 159: 1 – 3, 9 – 19, 24.
P138: 3 – 4.
HW #21: P157 – 159: 3, 5, 7, 8, 10 – 15, 22, 23.
P138: 7, 15.
Objectives: Know the terms parallel and skew
Know the Alternate Interior Angles theorem, Corresponding Angles Postulate,
Alternate Exterior Angles theorem and Consecutive Interior Angles theorem.
Lesson 22 – Aim: How do we prove that two lines are parallel? (Day 1) (Section 3.3)
HW #22: P165–166: 3, 5, 7, 8, 10–15, 22, 23.
P138: 8, 15.
Objectives: Know how to prove two lines cut by a transversal are parallel by using the
Alternative Interior Angles Converse, Corresponding Angles Converse, Alternative
exterior Angles Converse and the Consecutive Interior Angles Converse.
Lesson 22 – Aim: How do we prove two lines are parallel? (Day 2) (Section 3.3)
HW #22b: P165–168: 4, 8, 19–20, 23, 28, 34, 35*(CHALLENGING)
Objectives: Know how to prove two lines cut by a transversal are parallel by using the
Alternative Interior Angles Converse, Corresponding Angles Converse, Alternative
Exterior Angles Converse and the Consecutive Interior Angles Converse in twocolumn proofs
Lesson 23 – Aim: How do we find and use the slopes of lines? (Day 1) (Section 3.4)
HW #23: P175 – 177: 2 – 10, 17 – 19.
P138: 9, 10, 21
Objectives: Know how to find the slope of a line determined by two points
Know how to graph a line when given a slope and a point
Lesson 24 – Aim: How do we find and use the slopes of lines? (Day 2): (Section 3.4)
HW #24: P175 – 178: 13 – 16, 23 – 25, 27 – 29, 42.
P150: 3 – 6.
Objectives: know when two lines are parallel, perpendicular or neither using their slopes
Lesson 25 – Aim: How do we find and use the slopes of lines? (Day 3): (Section 3.4)
HW #25: FINSIH WORKSHEET
Objectives: know how to graph a line through a point that is parallel or perpendicular to a given
line
Lesson 26 – Aim: How do we write and graph the equations of lines? (Day 1) (Section 3.5)
HW #26: P184: 3 – 5, 9 – 12.
P166: 21, 24, 31.
P175-177: 7, 27 – 28
Objectives: know what is the slope-intercept form and turn any given linear equation into this
form
Know how to graph a linear equation
Know how to write the equation of a line when the graph is given
Lesson 27—Aim: How do we write and graph the equations of lines? (Day 2) (Section 3.5)
HW #27: P184 – 186: 17 – 18, 20, 23, 28, 31, 34, 36, 41
P176: 31
Objectives: how to write the equation of a line when two points are given
How to write an equation that is parallel or perpendicular to a given line.
Lesson 28—Aim: How do we prove theorems about perpendicular lines (day 1)? (Section 3.6)
HW #28: P194-197: 1-7, 16-17, 26, 32; P185: 49, 51
Lesson 29—Aim: How do we prove theorems about perpendicular lines (day 2)? (Section 3.6)
HW #29: P194-197: 8-10, 13, 14, 29, 34-38
Objectives: how to reason and write proof about theorems on parallel and perpendicular lines.
Ch 3 Review/ Uniform Unit Test
Common Core Standards Addressed
G-CO.1
Know precise definitions of angle, circle, perpendicular line, parallel line, and line
segment, based on the undefined notions of point, line, distance along a line, and distance
around a circular arc.
G-CO.9
Prove theorems about lines and angles. Theorems include: vertical angles are congruent;
when a transversal crosses parallel lines, alternate interior angles are congruent and
corresponding angles are congruent; points on a perpendicular bisector of a line segment
are exactly those equidistant from the segment’s endpoints.
G-CO.12 Make formal geometric constructions with a variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
Copying a segment; copying an angle; bisecting a segment; bisecting an angle;
constructing perpendicular lines, including the perpendicular bisector of a line segment;
and constructing a line parallel to a given line through a point not on the line.
G-GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve
geometric problems (e.g., find the equation of a line parallel or perpendicular to a given
G-GM.3
line that passes through a given point).
Apply geometric methods to solve design problems (e.g., designing an object or structure
to satisfy physical constraints or minimize cost; working with typographic grid systems
based on ratios).
Methods of Differentiated Instructions
Revolution K-12, a student-driven online learning platform, is used to differentiate instruction for all
students in class and subject areas.
All students are held to the Common Core-aligned standards. Teacher performs formative assessments
through lessons to check student understanding, including cold-calling, student board work, and exit
tickets. Teacher circulates room to perform further formative assessments and to guide small groups and
individuals.
Lower-performing students are grouped heterogeneously with higher-performing students using
assessment data, interests, and work habits, to encourage student-to-student engagement and learning.
They are also provided guided notes and graphic organizers to build schemas.
English Language Learners are paired with students who are fluent in English, and given extra time.
Vocabulary is pronounced several times and accompanied by alternative words or phrases that are
simplified. Visual aids, including pictures, Smart boards, and manipulatives, help students make clear
connections to the text.
Students with Special Needs are grouped with helpers and given instructions or assessments with
simplified language or extra time. Color-coding on the Smart board help illustrate steps required to solve
a problem. Hands-on activities are provided to help construct student learning.
Gifted/Honor students are given challenge problems during lessons, homework, and summative
assessments, which earn extra credits. They are expected to complete the whole worksheet, and are
given challenge (e.g. open-ended) problems that develop higher-level thinking.
Geometry Ch 4
Class website: http://PassGeometry.weebly.com
To receive full credits, you must copy or summarize the questions, copy all diagrams, and
construct all line drawings using a straightedge. Graphing must be done on graph paper.
Attend tutoring (and have logs signed) for extra credits.
Lesson 30 – Aim: How do we apply the triangle sum properties? (Section 4.1)
HW #30: P221: 7, 11, 13, 15, 18, 27, 32, 34.
P144: 4; P214: 8
Lesson 31 – Aim: What are the properties of congruent triangles? (Section 4.2)
HW #31: P228: 2 – 3, 5 – 10, 16, 17, 20, 26, 32*(Challenging)
P221: 1 – 6.
Lesson 32 – Aim: How do we prove triangles are congruent using SSS congruence postulate? (Section
4.3)
HW #32: P236: 1 – 7, 13 – 14**, 17, 18, 25 – 26. **Read P236
Lesson 33 – Aim: How do we prove triangles are congruent using SAS congruence postulate? (Section
4.4)
HW #33: P243 – 244: 2 – 5, 10 – 13, 21, 26, 36**Challenging
Lesson 34 – Aim: How do we prove triangles are congruent using HL congruence theorem? (Section
4.4)
HW #34: P243 – 244: 14, 22, 25, 27, 34, 37, 38.
Lesson 35&36 – Aim: How do we prove triangles are congruent using ASA congruence postulate and
AAS congruence theorem? (Section 4.5)
HW #35&36: P254 – 255: 25, 34
P244: 35
Lesson 37 – Aim: How do we prove triangles are congruent?
HW #37: FINISH WORKSHEET.
Lesson 38 – Aim: How do we prove corresponding parts of congruent triangles are congruent? (Section
4.6)
HW #38: P259: 3 – 6, 10 – 11, 22, 31
Lesson 39 – Aim: How do we prove corresponding parts of congruent triangles are congruent? (Section
4.6)
HW #39: P259: 8, 16, 23.
P238: 27
Lesson 40 – Aim: How do we apply the properties of isosceles and equilateral triangles? (Section 4.7)
HW #40: P267: 1 – 3, 6, 15 – 17, 45; P263: 5
CH 4 Review/Uniform Unit Test
At the end of this unit, you should be able to
1) know how to prove the Triangle Sum Theorem
2) know and apply the Exterior Angles Theorem and Triangle Sum Theorem
3) know that if two polygons are congruent, then their corresponding parts are congruent, and vice versa.
4) use shortcut SSS Congruence Postulate to prove two triangles are congruent.
5) use shortcut SAS Congruence Postulate to prove two triangles are congruent.
6) use shortcut ASA Congruence Postulate to prove two triangles are congruent.
7) use shortcut AAS Congruence Theorem to prove two triangles are congruent.
8) use shortcut HL Congruence Theorem to prove two triangles are congruent.
9) know that we can’t prove two triangles are congruent by using SSA  SSA or AAA  AAA .
10) know that in order to prove the corresponding angles or corresponding sides of two triangles are
congruent, it is necessary to prove the two triangles are congruent first using the properties and shortcuts
in steps 3 – 8
11) prove two corresponding angles or corresponding sides are congruent using CPCTC.
12) know the Base Angles Theorem and the Converse of the Base Angles Theorem.
13) know vertical angles are congruent, angles or segments that get bisected result in two smaller
congruent angles or segments, perpendicular lines form right angles,
14) apply the reflexive property.
15) know to apply the properties of two parallel lines cut by a transversal in your proof.
Common Core Standards Addressed
G-CO.7
Use the definition of congruence in terms of rigid motions to show that two triangles are
congruent if and only if corresponding pairs of sides and corresponding pairs of angles are
congruent.
G-CO.8
G-CO.9
G-CO.10
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the
definition of congruence in terms of rigid motions.
Prove theorems about lines and angles. Theorems include: vertical angles are congruent;
when a transversal crosses parallel lines, alternate interior angles are congruent and
corresponding angles are congruent; points on a perpendicular bisector of a line segment
are exactly those equidistant from the segment’s endpoints.
Prove theorems about triangles. Theorems include: measures of interior angles of a
triangle sum to 180°; base angles of isosceles triangles are congruent; the segment
joining midpoints of two sides of a triangle is parallel to the third side and half the length;
the medians of a triangle meet at a point.
Methods of Differentiated Instructions
Revolution K-12, a student-driven online learning platform, is used to differentiate instruction for all
students in class and subject areas.
All students are held to the Common Core-aligned standards. Teacher performs formative assessments
through lessons to check student understanding, including cold-calling, student board work, and exit
tickets. Teacher circulates room to perform further formative assessments and to guide small groups and
individuals.
Lower-performing students are grouped heterogeneously with higher-performing students using
assessment data, interests, and work habits, to encourage student-to-student engagement and learning.
They are also provided guided notes and graphic organizers to build schemas.
English Language Learners are paired with students who are fluent in English, and given extra time.
Vocabulary is pronounced several times and accompanied by alternative words or phrases that are
simplified. Visual aids, including pictures, Smart boards, and manipulatives, help students make clear
connections to the text.
Students with Special Needs are grouped with helpers and given instructions or assessments with
simplified language or extra time. Color-coding on the Smart board help illustrate steps required to solve
a problem. Hands-on activities are provided to help construct student learning.
Gifted/Honor students are given challenge problems during lessons, homework, and summative
assessments, which earn extra credits. They are expected to complete the whole worksheet, and are
given challenge (e.g. open-ended) problems that develop higher-level thinking.
Geometry Ch 5
Class website: http://PassGeometry.weebly.com
To receive full credits, you must copy/summarize questions, copy diagrams,
and construct using a straightedge and compass.
You will need your own ruler and compass for the Regents, so buy them now.
5 full tutoring sessions = 10% on a test, or 2 HW passes
A review booklet will be provided to you. You may use it on the test, so fill it out.
Lesson 42–Aim: What is the mid-segment theorem? (Section 5.1) 2 Days
HW #42: P298: 3, 5, 7, 9, 11, 25 – 27, 29*Challenging
Lesson 43 – Aim: What are the properties of perpendicular bisectors of a triangle? (Section 5.2) 2 Days
HW #43: P306 – 309: 3 – 5, 11 – 14, 26
Lesson 44 – Aim: What is the circumcenter? (Section 5.2)
HW #44: P306: 16 – 19
Lesson 45 – Aim: What are the angle bisector theorem and its applications? (Section 5.3)
HW #45: P313: 12 – 13, construct the angle bisector any obtuse angle.
construct the angle bisector any acute angle.
Bring a triangle cutout. It must be straight sides and big.
Lesson 46 – What is the incenter of a triangle?
HW #46: P314: 19, 20, 23, 24, construct the incenter of any triangle
Lesson 47 – Aim: What are the medians of a triangle? (Section 5.4)
HW #47: P322 – 324: 7, 10, 33 – 35, 41*
Lesson 48 – Aim: What are the altitudes of a triangle? (Section 5.4)
HW #48: Construct an altitude to AB from a point P above AB
Construct the orthocenter of an obtuse triangle.
Lesson 49 – Aim: What is the Triangle Inequality? (Section 5.5)
HW #49: P331: 2, 7 – 9, 16 – 18, 21 – 23, 31**. **Need to use calculator
Review booklet can be used on the test, but must be completed before the test
Ch 5 Review/Uniform Unit Test
At the end of this unit, you should be able to
1) know what is a mid-segment; know and apply the Mid-segment Theorem on triangles.
2) know what the perpendicular bisector does to a segment; know and apply the Perpendicular Bisector
Theorem and its converse.
3) know that the concurrency of three perpendicular bisectors is the circumcenter in a triangle and solve
problems involving the circumcenter.
4) know and apply the Triangle Inequality Theorem:
a) which three side lengths can (and cannot) make up a triangle
b) the possible length for the third side
5) know what an angle bisector does to an angle; know and apply the Angle Bisector Theorem and its
converse.
6) know that the concurrency of three angle bisectors is the incenter and solve problems involving the
incenter.
7) know the concurrency of three medians is the centroid and solve problems involving the centroid.
8) know the concurrency of the three altitudes forms the orthocenter.
9) construct a perpendicular bisector, a median, an angle bisector and an altitude using a compass and a
straightedge.
10) know that within a triangle, the longest side is always opposite the largest angle, the second longest
side is always opposite the second largest angle and the shortest side is always opposite the smallest
angle.
Common Core Standards Addressed
G-CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a
triangle sum to 180°; base angles of isosceles triangles are congruent; the segment
joining midpoints of two sides of a triangle is parallel to the third side and half the length;
the medians of a triangle meet at a point.
G-CO.12 Make formal geometric constructions with a variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
Copying a segment; copying an angle; bisecting a segment; bisecting an angle;
constructing perpendicular lines, including the perpendicular bisector of a line segment;
and constructing a line parallel to a given line through a point not on the line.
G-CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Construct the inscribed and circumscribed circles of a triangle.
G-C.3
G-MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure
to satisfy physical constraints or minimize cost; working with typographic grid systems
based on ratios)._
Methods of Differentiated Instructions
Revolution K-12, a student-driven online learning platform, is used to differentiate instruction for all
students in class and subject areas.
All students are held to the Common Core-aligned standards. Teacher performs formative assessments
through lessons to check student understanding, including cold-calling, student board work, and exit
tickets. Teacher circulates room to perform further formative assessments and to guide small groups and
individuals.
Lower-performing students are grouped heterogeneously with higher-performing students using
assessment data, interests, and work habits, to encourage student-to-student engagement and learning.
They are also provided guided notes and graphic organizers to build schemas.
English Language Learners are paired with students who are fluent in English, and given extra time.
Vocabulary is pronounced several times and accompanied by alternative words or phrases that are
simplified. Visual aids, including pictures, Smart boards, and manipulatives, help students make clear
connections to the text.
Students with Special Needs are grouped with helpers and given instructions or assessments with
simplified language or extra time. Color-coding on the Smart board help illustrate steps required to solve
a problem. Hands-on activities are provided to help construct student learning.
Gifted/Honor students are given challenge problems during lessons, homework, and summative
assessments, which earn extra credits. They are expected to complete the whole worksheet, and are
given challenge (e.g. open-ended) problems that develop higher-level thinking.
Corrected Geometry Ch 6 Homework Sheet
Class website (lesson handout and homework answers): http://PassGeometry.weebly.com
To receive full credits, you must copy/summarize questions,and copy diagrams using rulers.
You will want a good ruler and compass (Safe-T compass $2 at Staples) for the Regents.
5 full tutoring sessions = 10% on a test, or 3 HW passes
Saturday Academy on Jan. 11 and 25, 08:30 to 11:30
(1 tutoring credit per half an hour! That’s 10% test grade in one day.)
Lesson 50 – Aim: How do we solve problems involving ratios, proportions and the geometric mean?
(Section 6.1)
HW #50: P360 – 362: 18 – 21, 23, 25, 30, 31, 33, 35, 53, 56*(Challenging)
Lesson 51 – Aim: What are the properties of similar polygons (Section 6.3)
HW #51: P376 – 378: 1, 3, 5, 6, 8 – 10, 14 – 18.
Lesson 52 – Aim: How do we prove triangles similar by AA Similarity Postulate? (Section 6.4)
HW #52: P384 – 385: 1, 3 – 12, 15, 16, 20.
Lesson 53 – Aim: How do we prove triangles similar by AA Similarity Postulate? (Section 6.4)
HW #53: Finish worksheet
Lesson 54 – Aim: How do we prove triangles similar by SSS Similarity Theorem? (Section 6.5)
HW #54: P391 – 393: 3 – 6, 10, 15, 26*(Challenging)
Lesson 55 – Aim: How do we prove triangles similar by SAS Similarity Theorem? (Section 6.5)
HW #55: P391: 7 – 9, 11 – 12, 14, 31.
Lesson 56 – Aim: What is the Triangle proportionality Theorem? (Section 6.6)
HW #56: Finish worksheet
Lesson 57 – Aim: How do we compare the perimeters and areas of similar figures? (Section 11.3)
HW #57: P740 – 741: 3 – 5, 9, 11, 13, 14, 22.
Ch 6 Review/Uniform Unit Test
Regents Review
Mid-term Final
At the end of this unit, you should be able to
1) know how to set up and solve an equation involving ratios.
2) know how to calculate the geometric mean.
3) know the properties of similar polygons: corresponding angles are congruent but corresponding side
lengths are proportional.
4) know how to set up a proportion to solve the length of a corresponding side or a corresponding angle
in similar polygons
5) know that two triangles are similar if two pairs of corresponding angles are congruent: AA  AA or
AA Similarity Theorem; prove two triangles are similar by AA Similarity Theorem.
6) find the missing angle measure to show that two triangles are similar by AA Similarity Theorem.
7) know that two triangles are similar if three pairs of corresponding sides have the same ratio: SSS
Similarity Theorem; prove two triangles are similar by SSS Similarity Theorem.
8) find the missing length to show that two triangles are similar by SSS Similarity Theorem.
9) know that two triangles are similar if the lengths of two corresponding sides have the same ratio and
the included angles are congruent: SAS Similarity Theorem.
10) find the missing length to show that two triangles are similar by SSS Similarity Theorem.
11) know the relationship between the ratio of the perimeters and the ratio of corresponding sides of
similar polygons, and solve problems involving these ratios.
12) know the relationship between the ratio of the areas and the ratio of corresponding sides of similar
polygons, and solve problems involving these ratios.
13) know how to prove and apply the Triangle Proportionality Theorem and its converse.
Common Core Standards Addressed
G-CO.2
Represent transformations in the plane using, e.g., transparencies and geometry
software; describe transformations as functions that take points in the plane as inputs
and give other points as outputs. Compare transformations that preserve distance and
angle to those that do not (e.g., translation versus horizontal stretch).
G-SRT.1
Verify experimentally the properties of dilations given by a center and a scale factor:
a. A dilation takes a line not passing through the center of the dilation to a parallel
line, and leaves a line passing through the center unchanged.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale
factor.
G-SRT.2
G-SRT.3
G-SRT.4
G-SRT.5
G-C.1
G-MG.3
Given two figures, use the definition of similarity in terms of similarity
transformations to decide if they are similar; explain using similarity transformations
the meaning of similarity for triangles as the equality of all corresponding pairs of
angles and the proportionality of all corresponding pairs of sides.
Use the properties of similarity transformations to establish the AA criterion for two
triangles to be similar.
Prove theorems about triangles. Theorems include: a line parallel to one side of a
triangle divides the other two proportionally, and conversely; the Pythagorean
Theorem proved using triangle similarity.
Use congruence and similarity criteria for triangles to solve problems and to prove
relationships in geometric figures.
Prove that all circles are similar.
Apply geometric methods to solve design problems (e.g., designing an object or
structure to satisfy physical constraints or minimize cost; working with typographic
grid systems based on ratios).
Methods of Differentiated Instructions
Revolution K-12, a student-driven online learning platform, is used to differentiate instruction for all
students in class and subject areas.
All students are held to the Common Core-aligned standards. Teacher performs formative assessments
through lessons to check student understanding, including cold-calling, student board work, and exit
tickets. Teacher circulates room to perform further formative assessments and to guide small groups and
individuals.
Lower-performing students are grouped heterogeneously with higher-performing students using
assessment data, interests, and work habits, to encourage student-to-student engagement and learning.
They are also provided guided notes and graphic organizers to build schemas.
English Language Learners are paired with students who are fluent in English, and given extra time.
Vocabulary is pronounced several times and accompanied by alternative words or phrases that are
simplified. Visual aids, including pictures, Smart boards, and manipulatives, help students make clear
connections to the text.
Students with Special Needs are grouped with helpers and given instructions or assessments with
simplified language or extra time. Color-coding on the Smart board help illustrate steps required to solve
a problem. Hands-on activities are provided to help construct student learning.
Gifted/Honor students are given challenge problems during lessons, homework, and summative
assessments, which earn extra credits. They are expected to complete the whole worksheet, and are
given challenge (e.g. open-ended) problems that develop higher-level thinking.