Geometry Chapter 1 - CRHS Geometry Academic

Geometry Chapter 1
Notes & Worksheets
1st Six Weeks 2015-2016
MONDAY
August 24
TUESDAY
25
WEDNESDAY
26
27
Algebra Review
Algebra Review
Algebra Review
Multi-Step Eqns.
WS
Simplifying Radicals
WS
Solving Proportions
WS
31
Sept 1
THURSDAY
2
FRIDAY
28
1-1 Points, Lines and
Planes
1-2 Line Segments
and Distance
1-1 SP: 1-4, 9-12 p. 5
1-1 Prac: 1-4, 6-13 p.6
1-2 Prac: Odds & #2 p. 11
1-2 WP: 1, 2, 5 p. 12
3
4
1-3 Locating Points
and Midpoints
Constructions
(1 and 2 notes)
Quiz
1-1 through 1-3
1-4 Angle Measure
1-5 Angle
Relationships
1-3 Prac: 1-9 all,
11-21 odd p. 17
1-3 WP: 1, 2, 4 p. 18
Mid Chapter WS
Omit #5 and #10
p. 19
Complete
Constructions
1 and 2
1-4 SP: all p. 25
1-4 WP: #4 and #5
p. 26
1-5 Prac: 1-12 all p. 31
1-5 WP: 1, 3, 5 p. 32
7
8
NO SCHOOL
14
9
11
Constructions
(3, 4 and 5)
Quiz:
1-4 through 1-5
Activity
(Review)
Test:
Chapter 1
Complete
Constructions
Chapter 1 Test
Review #1 pp. 33-35
Chapter 1 Test
Review #2 p. 37-38
Chapter 2 Vocab
(in Ch. 2 Packet)
16
17
15
2-1 Inductive
Reasoning and
Conjecture
10
2-3 Conditional
Statements
18
2-4 Deductive
Reasoning
Activity
Quiz:
2-1 through 2-4
2-2 Logic
21
22
2-5 Postulates and
Paragraphs Proof
23
2-6 Algebraic
Proofs
24
2-7 Proving Segment
Relationships
25
Proof Blocks
Quiz:
2-5 through 2-8
2-8 Proving Angle
Relationships
28
29
Activity
(Review)
30
Test:
Chapter 2
Oct 1
3-1 Parallel Lines
and Transversals
3-2 Angles and
Parallel Lines
** All assignments are subject to change.
Cumulative Test
Chapters 1 and 2
2 Early Dismissal
Activity
1-1 Points, Lines and Planes
Number each Quadrant and label each axis.
2. Which quadrant is point C located in? _______
Point D? _______
Undefined Term - no formal ___________________ but it’s ____________________.
Undefined terms have no definite _______________ or _________________.
______________ - an _____________ _______________ in space and is ______________
by a ________.
Picture:
Written as: _________________________
1
_____________ - collection of _____________ along a __________________ ___________
extending _______________ in _________________ directions.
Written as: _________________________
Picture:
There is _________ __________ line through any __________ __________.
_____________ - _________ surface extending ______________ in all directions.
Written as: _________________________
Picture:
There is _________ __________ plane through any __________ __________ not on
the same line
_____________ - Points that ____________ on the ______________ ______________.
Picture:
Picture:
2
_____________ - Points that _____ ______ lie on the _____________ ________________.
Picture:
**All it takes is for _______ point
within the set of points to be
_____ of the line to be considered
_________________________.
_____________ - Points that ____________ in the ______________ ______________.
Picture:
Picture:
_____________ - Points that _____ ______ lie in the _____________ ________________.
Picture:
**All it takes is for _______ point
within the set of points to be
_____ of the plane to be
considered
Intersections of Geometric Figures:
Intersection – set of common point(s) that two or more geometric figures share.
•
_____________ lines intersect at a ______________.
Picture:
Line m intersects line k at point F
3
•
A __________ and a ______________ intersect at a
Picture:
________________.
Line k intersects plane A at point B
•
_____________ planes intersect at a ______________.
Picture:
Plane M and plane C intersect at line AB
4
NAME
1-1
DATE
PERIOD
Skills Practice
Points, Lines, and Planes
Refer to the figure.
A
1. Name a line that contains point e.
D
B
p
n
G
C
2. Name a point contained in line n.
Lesson 1-1
e
q
3. What is another name for line p?
4. Name the plane containing lines n and p.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Draw and label a figure for each relationship.
.
5. Point K lies on RT
6. Plane J contains line s.
lies in plane B and contains
7. YP
point C, but does not contain point H.
8. Lines q and f intersect at point Z
in plane U.
F
Refer to the figure.
9. How many planes are shown in the figure?
D
E
A
C
W
B
10. How many of the planes contain points F and E?
11. Name four points that are coplanar.
12. Are points A, B, and C coplanar? Explain.
Chapter 1
5
Glencoe Geometry
NAME
1-1
DATE
PERIOD
Practice
Points, Lines, and Planes
Refer to the figure.
1. Name a line that contains points T and P.
j
M
P
2. Name a line that intersects the plane containing
points Q, N, and P.
Q
T
R
S
N
h
g
.
and QR
3. Name the plane that contains TN
Draw and label a figure for each relationship.
intersect at point M
and CG
4. AK
in plane T.
5. A line contains L(-4, -4) and M(2, 3).
Line q is in the same coordinate plane but
. Line q contains
does not intersect LM
point N.
y
x
O
T
6. How many planes are shown in the figure?
W
7. Name three collinear points.
A
8. Are points N, R, S, and W coplanar? Explain.
Q
P
S
X
R
M
N
VISUALIZATION Name the geometric term(s) modeled by each object.
9.
STOP
12. a car antenna
Chapter 1
10.
tip of pin
11.
strings
13. a library card
6
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Refer to the figure.
1-2 Line Segments and Distance
_________ ________________ - part of a line ______________ of ________ ____________
and all __________ on the line ______________ the endpoints.
Picture:
Written as: _________________________
The length of a segment is the _____________________ between its _______ ________________.
•
Draw an example of a point that would be between A and C.
The measure of AB is written as __________.
** It is the ____________ between _______ and _______. So the measure of a
___________ is
the same as the ___________________ ______________________ its two endpoints.
Congruence:
Congruent means same __________ and same ___________ and its symbol is _________.
Congruent segments - ___________ segments that have the ____________ ________________.
7
The Ruler Postulate (Distance formula on a number line):
The numbers on a ruler are a __________________________ example of a ___________________.
The __________________ between two points on a number line is the ______________ _________
of the difference of the coordinates. It can be found using:
AB = __________________________
EX 1:
Distance from X to Y can be written as: ___________________ OR _______________________.
EX 2: Find PQ, QR, and PR if P is located at -3, Q is located at 1, and R is located at 6.
Distance Formula (in Coordinate Plane):
The ___________ between two points (x1, y1) and (x2, y2) on a coordinate plane can be found using the
__________ ___________.
d = ________________________
8
Example 3: Find the distance between the points M (2, 4) and N (-3, -2).
���� are congruent.
Example 4: Determine if the two segments ����
𝐴𝐴𝐴𝐴 and 𝐿𝐿𝐿𝐿
����
𝐴𝐴𝐴𝐴: A (4, 6) and B (7, 2)
����
𝐿𝐿𝐿𝐿: L (-1, -6) and K (4, -6)
9
10
NAME
DATE
1-2
PERIOD
Practice
Line Segments and Distance
Find the measurement of each segment. Figures are not drawn to scale.
−−
1. PS
−−−
2. AD
18.4 cm
−−−
3. WX
2 3–8 in.
4.7 cm
P
Q
S
A
1 1–4 in.
C
W
X
Y
89.6 cm
100 cm
D
Geo-PR01-02-11-846589
Geo-PR01-02-13-846589
Geo-PR01-02-12-846589
ALGEBRA Find the value of x and KL if K is between J and L.
4. JK = 6x, KL = 3x, and JL = 27
5. JK = 2x, KL = x + 2, and JL = 5x - 10
Determine whether each pair of segments is congruent.
−−− −−−
7. AD, BC
T 2 ft S
2 ft
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
U
−−− −−
8. GF, FE
12.7 in.
A
B
5x
G
H
3 ft
3 ft
6x
D
W
C
12.9 in.
Use the number line to find each measure.
9. VW
S
–10
10. TV
Find the distance between each pair of points.
Z
M
–8
–6
y
O
x
E
Geo-PR01-02-16-846589
T
U
–4
–2
V
0
W
2
4
6
8
Geo-SG01-03-05-846589
12.
y
O
F
Geo-PR01-02-15-846589
Geo-PR01-02-14-846589
11.
Lesson 1-2
−−− −−−
6. TU, SW
S
x
E
Geo-PR01-03-07-846589
Geo-PR01-03-06-846589
13. L(-7, 0), Y(5, 9)
Chapter 1
14. U(1, 3), B(4, 6)
11
Glencoe Geometry
NAME
1-2
DATE
PERIOD
Word Problem Practice
Line Segments and Distance
1. WALKING Marshall lives 2300 yards
from school and 1500 yards from the
pharmacy. The school, pharmacy, and
his home are all collinear, as shown in
the figure.
4. BUILDING BLOCKS Lucy’s younger
brother has three wooden cylinders.
They have heights 8 inches, 4 inches,
and 6 inches and can be stacked one on
top of the other.
2300 yards
1500 yards
School
Pharmacy
Home
What is the total distance from the
pharmacy to the school?
8 in.
[C01-06A-873958]
4 in.
6 in.
a. If all three cylinders are stacked one
on top of the other, how high will the
resulting
column be? Does it matter
[C01-07A-873958]
in what order the cylinders are
stacked?
2. RAILROADS A straight railroad track is
being built to connect two cities. The
measured distance of the track between
the two cities is 160.5 miles. A mailstop
is 28.5 miles from the first city. How far
is the mailstop from the second city?
y
O
x
5. WASHINGTON, D.C. The United States
Capitol is located 800 meters south and
2300 meters to the east of the White
House. If the locations were placed on a
coordinate grid, the White House would
be at the origin. What is the distance
between the Capitol and the White
House? Round your answer to the
nearest meter.
[C01-09A-873958]
Chapter 1
12
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
b. What are all the possible heights of
columns that can be built by stacking
some or all of these cylinders?
3. SPIRALS Caroline traces out the spiral
shown in the figure. The spiral begins at
the origin. What is the shortest distance
between Caroline’s starting point and
her ending point?
1-3 Locating Points and Midpoints
What is the coordinate of the midpoint XY?
13
____________ means to __________ in ____________.
14
EX 4: The endpoints of RS are R(1, -3) and S(4, 2). Find the midpoint.
EX 5:
EX 6: What happens when you are missing an endpoint?
The midpoint of JK is M(2, 1). One endpoint is J(1, 4).
Find the coordinates of endpoint K.
15
Locating a Point at Fractional Distances:
���� that is
Example 7: Find X on 𝐴𝐴𝐴𝐴
1
of the distance from A (-7) to F (5). Graph A and F on the number line below.
6
(Note: “from A to F” indicates that A is the starting point.)
Example 8: Find R on NM that is
1
the distance from N (-3, -3) to M (2,3).
4
16
NAME
1-3
DATE
PERIOD
Practice
Locating Points and Midpoints
Use the number line to find the coordinate
of the midpoint of each segment.
P
–10
−−−
2. QR
−−
4. PR
−−
1. RT
−−
3. ST
Q
–8
–6
R
–4
S
–2
T
0
2
4
6
Geo-SG01-03-08-846589
Find the coordinates of the midpoint of a segment with the given endpoints.
5. K(-9, 3), H(5, 7)
6. W(-12, -7), T(-8, -4)
−−
Find the coordinates of the missing endpoint if E is the midpoint of DF.
7. F(5, 8), E(4, 3)
8. F(2, 9), E(-1, 6)
9. D(-3, -8), E(1, -2)
Use the number line to find the coordinate
of the point the given fractional distance
from A to B.
1
11. −
3
3
15. −
5
1
12. −
A
-8 -7 -6 -5 -4 -3 -2 -1 0
1
13. −
5
2
16. −
3
B
6
5
17. −
6
1
2
3
4
5
6
Lesson 1-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10. PERIMETER The coordinates of the vertices of a quadrilateral are R(-1, 3), S(3, 3),
T(5, -1), and U(-2, -1). Find the perimeter of the quadrilateral. Round to the
nearest tenth.
1
14. −
4
P21-001A-890857
3
18. −
4
−−−
Find P on NM that is the given fractional distance from N to M.
3
, N(1, 7), M(9, -2)
19. −
4
20. −
, N(-4, 5), M(2, -6)
4
2
, N(-3, -4), M(6, 3)
21. −
5
5
1
22. −
, N(-4, 2), M(7, 9)
3
Refer to the graph at the right.
y
−−
23. Find C on AB such that the ratio of AC to CB is 1:2.
B
4
2
−−
24. Find C on AB such that the ratio of AC to CB is 4:3.
-4
-2
O
2
4x
-2
A
Chapter 1
021_GEOCRMC01_715477.indd 21
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NAME
1-3
DATE
PERIOD
Word Problem Practice
Locating Points and Midpoints
1. CAMPGROUND Troop 175 is designing
their new campground by first mapping
everything on a coordinate grid. They
have found a location for the mess hall
and for their cabins. They want the
bathrooms to be halfway between these
two. What will be the coordinates of the
location of the bathrooms?
4. MAPPING Ben and Kate are making a
map of their neighborhood on a piece of
graph paper. They decide to make one
unit on the graph paper correspond to
100 yards. First, they put their homes
on the map as shown below.
y
Ben’s
House
y
Cabins
O
O
Mess Hall
Kate’s
House
2. PIZZA Calvin’s home is located at the
midpoint between Fast Pizza and Pizza
Now. Fast Pizza is a quarter mile away
from Calvin’s
home. How far away is
[C01-08A-873958]
Pizza Now from Calvin’s home? How far
apart are the two pizzerias?
8
y
Home Town
4
-4
O
4
8x
-4
a. How many yards apart are Kate’s
and Ben’s homes?
[C01-10A-873958]
b. Their friend Jason lives exactly
halfway between Ben and Kate. Mark
the location of Jason’s home on the
map.
5. DECORATING Steve and Abby
purchased a set of vases to place on a
12-foot long mantel above their fireplace.
They want to place one vase 1/4 of the
distance from one end of the mantel and
the other vase 3/4 of the distance from
the same end. How many feet from the
end of the mantel should each vase be
placed?
-8
San Antonio
a. If the girls take turns driving and
each girl drives the same distance, at
what point should they stop for Emily
to begin her turn as the third driver?
b. At what point does Emily’s turn to
drive end?
Chapter 1
18
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. ROADTRIP Stephanie, Andrea, Emily,
and Becca are planning a road trip from
their home town to San Antonio, Texas
as shown on the graph below.
-8
x
x
NAME
DATE
1
Chapter 1 Mid-Chapter WS
PERIOD
SCORE
(Lessons 1-1 through 1-4)
For Exercises 1 and 2, refer to the figure.
E
1. Which point is collinear with points A and C?
A A
C C
B B
1.
J M
2.
Geo-AS01-54-846589
A
B
-6 -5 -4 -3 -2 -1 0
D 2
1
2
3
4
5
6
7
8
9 10
3.
P53-001A-890857
5.8 cm
−−−
4. Find the measure of NL.
F 2.1 cm
H 3.7 cm
G 3.2 cm
J 7.9 cm
Copyright © Glencoe∠McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
C
D
.
2. Name the point of intersection of plane M and DE
F D
G E
H B
B 0
M
B
A
D D
3. What is the coordinate of the
2
point −
of the distance from A to B?
3
A 8
C 4
Assessment
Part I Write the letter for the correct answer in the blank at the right of each question.
2.1 cm
M
N
L
4.
5. Ray NP is an angle bisector of ∠MNQ and m∠PNQ = 2x + 1.
Find m∠MNQ.
C01-010A-890510
2x + 1
A 4x + 1
B 2x + 2
C 4x + 2
D −
5.
2
Part II
For Exercises 6–8, use the coordinate grid.
y
R
6. Find the distance between R and S.
O
−−−
7. Find the coordinates of the midpoint of TU.
U
S
x
6.
7.
T
3
of the
8. Find the coordinates of a point M −
4
distance from T to S.
8.
6y + 5
9yGeo-AS01-57-846589
-4
9. Find the value of y if M is the
−−−
midpoint of LN.
L
M
N
9.
10. A giant slingshot is formed with ends held at Geo-AS01-58-846589
points A and C.
Barb has stretched it back and is holding it at point B. Donny
Daredevil stands at the midpoint of the line segment AC. On
which part of the angle formed by the slingshot does
10.
Donny lie?
Chapter 1
053_GEOCRMC01_715477.indd 53
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2nd Pass
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20
1-4 Angle Measure
_________________ - part of a line with ________ endpoint that extends
_________________ in the _________________ direction.
Written as: _________________________
Picture:
**CANNOT be written as _____. The
endpoint is always the first letter
written in the notation for a ray. The
direction the ray is pointing is always
the 2nd letter written.
___________________ __________ are rays that share an ___________ and extend in
______________ directions along the same line.
21
F
Point ____, ____ and ____ lie on angle CPE.
Points ____ and ____ lies in the exterior of angle CPD .
Point ____ lies in the interior of angle CPE.
EX 1:
22
EX 2:
EX 3:
EX 4:
23
24
NAME
1-4
DATE
PERIOD
Skills Practice
Angle Measure
For Exercises 1–12, use the figure at the right.
U
Name the vertex of each angle.
4
S
1. ∠4
2. ∠1
3. ∠2
3
5
T
1
2V
W
4. ∠5
Name the sides of each angle.
5. ∠4
6. ∠5
7. ∠STV
8. ∠1
Write another name for each angle.
9. ∠3
10. ∠4
12. ∠2
Classify each angle as right, acute, or obtuse. Then use
a protractor to measure the angle to the nearest degree.
13. ∠NMP
14. ∠OMN
15. ∠QMN
16. ∠QMO
P
Q
O
L
M
N
⎯⎯ and BC
⎯⎯ are opposite
ALGEBRA In the figure, BA
E
⎯⎯ bisects ∠EBC.
rays, BD
F
17. If m∠EBD = 4x + 16 and m∠DBC = 6x + 4,
find m∠EBD.
A
D
B
C
18. If m∠EBD = 4x - 8 and m∠EBC = 5x + 20,
find the value of x and m∠EBC.
Chapter 1
25
Glencoe Geometry
Lesson 1-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11. ∠WTS
NAME
DATE
1-4
PERIOD
Word Problem Practice
Angle Measure
5. ROADS Central Street runs north-south
and Spring Street runs east-west.
er
Riv
St.
Central St.
1. LETTERS Lina learned about types of
angles in geometry class. As she was
walking home she looked at the letters
on a street sign and noticed how many
are made up of angles. The sign she
looked at was KLINE ST. Which
letter(s) on the sign have an obtuse
angle? What other letters in the
alphabet have an obtuse angle?
(x + 8)˚
3. STARS Melinda wants to know the
angle of elevation of a star above the
horizon. Based on the figure, what is the
angle of elevation? Is this angle an
acute, right, or obtuse angle?
1
110
80
90
0
14
30
15
0
20
160
20
0
b. Valerie is driving down Spring Street
heading east. She takes a left onto
River Street. What type of angle did
she have to turn her car through?
c. What is the angle measure Valerie is
turning her car when she takes the
left turn?
160
10
170
10
13
30
0
180
O
a. What kind of angle do Central Street
and Spring Street make?
0
50
0
13
0
170
12
60
15
0
110
70
40
180
100
80
100
0
40
50
20
Spring St.
Lesson 1-4
70
60
14
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. SQUARES A square has four right
angle corners. Give an example of
another shape that has four right angle
corners.
(3x + 12)˚
4. CAKE Nick has a slice of cake. He
wants to cut it in half, bisecting the 46°
angle formed by the straight edges of the
slice. What will be the measure of the
angle of each of the resulting pieces?
Chapter 1
26
Glencoe Geometry
1-5 Angle Relationships
27
28
There are some things you can conclude from a diagram and some you cannot conclude.
29
30
NAME
1-5
DATE
PERIOD
Practice
Angle Relationships
Name an angle or angle pair that satisfies each condition.
G
H
50°
F
1. Name two obtuse vertical angles.
C
B
2. Name a linear pair whose vertex is B.
50°
3. Name an angle not adjacent to, but complementary
to ∠FGC.
A
E
D
4. Name an angle adjacent and supplementary to ∠DCB.
5. ALGEBRA Two angles are complementary. The measure of one angle is 21 more than
twice the measure of the other angle. Find the measures of the angles.
6. ALGEBRA If a supplement of an angle has a measure 78 less than the measure of the
angle, what are the measures of the angles?
ALGEBRA For Exercises 7–8, use the figure at
A
the right.
B
7. If m∠FGE = 5x + 10, find the value of x so that
⊥ AE
.
FC
C
G
F
E
Determine whether each statement can be
assumed from the figure. Explain.
N
O
9. ∠NQO and ∠OQP are complementary.
P
Q
M
10. ∠SRQ and ∠QRP is a linear pair.
R
Chapter 1
31
aco
12. STREET MAPS Darren sketched a map of the cross streets
nearest to his home for his friend Miguel. Describe two
different angle relationships between the streets.
Be
11. ∠MQN and ∠MQR are vertical angles.
n
S
Olive
Ma
in
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
D
8. If m∠BGC = 16x - 4 and m∠CGD = 2x + 13,
find the value of x so that ∠BGD is a right angle.
NAME
1-5
DATE
PERIOD
Word Problem Practice
Angle Relationships
1. LETTERS A sign painter is painting a
large “X”. What are the measures of
angles 1, 2, and 3?
4. GLASS Carlo dropped a piece of stained
glass and the glass shattered. He picked
up the piece shown on the left.
2
1
120˚
3
106˚
Part of edge
2
Missing Piece
He wanted to find the piece that was
adjoining on the right. What should the
measurement of the angle marked with
a question mark be? How is that angle
related to the angle marked 106°?
5. LAYOUTS A rectangular plaza has a
walking path along its perimeter in
addition to two paths that cut across the
plaza as shown in the figure.
Cut
1
3. PIZZA Ralph has sliced a pizza using
straight line cuts through the center of
the pizza. The slices are not exactly the
same size. Ralph notices that two
adjacent slices are complementary. If
one of the slices has a measure of 2xº,
and the other a measure of 3xº, what is
the measure of each angle?
1
135˚
3
2
4
50˚
a. Find the measure of ∠1.
b. Find the measure of ∠4.
c. Name a pair of vertical angles in the
figure. What is the measure of ∠2?
Chapter 1
32
Glencoe Geometry
Lesson 1-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. PAPER Matthew cuts a straight line
segment through a rectangular sheet of
paper. His cuts goes right through a
corner. How are the two angles formed
at that corner related?
?
Name: ____________________________________________ Date:_______________ Period:___
Geometry
Chapter 1 Test Review #1
Show all work (either on the worksheet or on separate paper that is attached).
20. Draw an example of vertical angles and a linear pair. Don’t forget to label your drawing.
33
21. Given that <JKM and <MKO make up a right angle. Solve for x, m<JKM, and m<MKO if
m<JKM = 2x +7 and m<MKO = 3x + 8.
22. What is another name for <JKM and <MKO from problem 21? ______________________
23. Find X on ����
𝐴𝐴𝐴𝐴 that is
line below.
1
of the distance from A (-5) to F (7). Graph A and F on the number
3
24. Find R on NM that is
1
the distance from N (-3, -4) to M (5,4).
4
34
24. Define the following terms:
a.
Point - _____________________________________________________________
b. Line - ______________________________________________________________
c. Plane - _____________________________________________________________
d. Collinear points - _____________________________________________________
e. Coplanar points - ______________________________________________________
f. Line segment - _______________________________________________________
g. Ray - ______________________________________________________________
h. Midpoint - __________________________________________________________
i. Segment bisector - ____________________________________________________
j. Angle bisector - ______________________________________________________
k. Supplementary angles - _________________________________________________
l. Complementary angles - ________________________________________________
m. Adjacent angles - _____________________________________________________
n. Linear pair - _________________________________________________________
o. Vertical angles - ______________________________________________________
35
36
Name:_________________________________________ Date: _________________ Period:____
Geometry
Chapter 1 Test Review #2
Read each question carefully. Show all work!
1.
The endpoints of two segments are given. Find the exact length of the segment.
CD = C(3, 4) , D(1, -1)
CD = ________
2.
Using the points from #1, find the midpoint of CD
Midpoint = ________
3.
The midpoint of LM is O(2, 1). One endpoint is L(1, 4). Find the coordinates of endpoint M.
Point M = _________
In exercises 4 – 8, use the diagram.
37
9. Given that < ABC and < DEF are complementary, find the value of x and the measure of each angle if
m< ABC = (4x + 3) ° and the m< DEF = (x -8) °
x = _______
m< ABC = _______
m< DEF = _______
10. Linear pairs are a special type of ______________________angles whose sum is _______.
11. < LMN and < NMR are a linear pair. If m< LMN = (7x + 10) ° and m< NMR = 3x ° , find the
value of x and the measure of each angle. Draw a picture!
x = _______
m< LMN = _______
m< NMR = _______
12. What word means “to cut in half”? ______________

13. The m< DEF is bisected by EB . Find the value of x and the measures of the angles if m< DEB =5x °
and m< BEF = (x +16) ° .
x = ______
m< DEB = _______
m< BEF = _______
For numbers 14-17, simplify the following radicals:
14.
80
15.
16. 5 48
288
38
17. −3 32