4-1 and 4-2 Review Worksheet

Transcription

4-1 and 4-2 Review Worksheet
NAME
DATE
PERIOD
Name ___________________________________ Hour ______
4-1
Skills Practice 4-1 and 4-2 Review Worksheet
Classifying Triangles
4-1 Classifying Triangles
Classify each triangle as acute, equiangular, obtuse, or right.
1.
60°
4.
2.
60°
60°
95°
90°
45°
50°
5.
50°
80°
3.
40°
40°
70°
6.
50°
30°
50°
55° 55°
100°
Classify each triangle as equilateral, isosceles, or scalene.
7. !ABE
8√2
8. !EDB
E
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9. !EBC
8
D
C
10. !DBC
11. ALGEBRA Find x and the length of
each side if !ABC is an isosceles
−−
−−
triangle with AB # BC.
12. ALGEBRA Find x and the length of each
side if !FGH is an equilateral triangle.
#
4x - 3
"
B
9
A
x+2
(
3x + 10
2x + 5
'
$
x =ALGEBRA
______________
13.
Find x and the length of
each side if !RST is an isosceles
−− −−
AB = _____________
triangle with RS # TS.
5x - 8
)
4x + 1
= _______________
14.x ALGEBRA
Find x and the length of each
side if !DEF is an equilateral triangle.
FG = _____________
BC = _____________
3
GH = _____________
&
9x + 2
AC = _____________
FH = ______________
3x - 1
5x - 21
2x + 6
4
6x + 8
5
Chapter 4
%
43
7x - 39
'
Glencoe Geometry
NAME
DATE
PERIOD 57°
ware
- Infinite Geometry
Name___________________________________
FNGLE
INDING
ANGLE
MFind
EASURES
Find
the
of the
numbered
NT HELP
FINDINGHA
MEASURES
the measure
ofmeasure
the
numbered
angles.
FINDING
ANGLE
M
EASURES
Find
the
measure
of theangles.
numbered angles.
STUDENT
ELP
Kuta
Software - Infinite Geometry
Name___________________________________
NET
HOMEWORK
31.
32.
33.
ER HELP
Pin a Triangle
31. HOMEWORK HELP 1
33. Date________________
31. 32.
32.
33.
Period____
1
1
4-1site
Triangle
Angle
Sum
Visit
1
1 our Web
1
site our Web
Visit
site
56!
Angles
in
a
Triangle
Date________________
Period____
56!
cdougallittell.com
56!
com
www.mcdougallittell.com
3
measure
of
each
angle
indicated.
3
2
Find
each
missing
angle.
with
Exs.
31–33.
3
of Triangles
50!
3
3
40!
2
3.
3
2
for help with Exs.Angles
31–33.
40!
50!
95!
40!50!
13. the measure
15.1 2
95! 14.
42! angle indicated.
95!45!
Find
of each
42!
1 45!2
42!
45!
1 2
Find the measure of each numbered
3)
2) angle.
?
1) LOGICAL
2)
LOGICAL
REASONINGComplete
Complete
the
statement
using
always,
sometimes,
REASONING
the
statement
using
always,
sometimes,
4-2
INT
Practice
1.xor never.
65°
2.
?
xy USING
A
The variable
expressions
represent
the angle
40°
xLGEBRA
USING
ALGEBRA
The
variable
the
angle
y EASONING
UOGICAL
SING Aexpressions
LGEBRA
Therepresent
variable
expressions
represent
the
anglesometimes,
LOGICAL
R
L
RComplete
EASONING
the
Complete
statement
the
using
always,
using
sometimes,
always,
orynever.
1statement
72° measures
of
a
triangle.
Find
the
measure
of
each
angle.
Then
classify the 20°
2 of
measures
triangle.
Find
the
measure
of each
angle.
Then40°
classify
the
or anever.
or
never.
measures
of
a
triangle.
Find
the
measure
of
each
angle.
Then
classify the
?
22.
An
isosceles
triangle
is
an
equilateral
triangle.
!!!!!
by its
?!!!!!!
22.
An isosceles
triangle
is angles.
an its
equilateral
!!!!!
triangle
bytriangle
its 1angles.
triangle
by
angles. triangle.
?!!! an
?!!! an
22. An
isosceles
22.
An
triangle
isosceles
is !!!!!
triangle
is !!!!!
equilateral
triangle.
equilateral
57°
40°
55°triangle.
?!!!
23.
obtuse
triangle
is !!!!!
isosceles
triangle.
?!!!
23.
AnAn
obtuse
triangle
isx°
anan
isosceles
triangle.
!!!!!
34.
m™A
=
35.
m™R
=
x°
36.
= 36.
(x º
15)° = (x º130°
?
34. m™A =23.
x° An obtuse
35.obtuse
m™R
=
x°an isosceles
36.
m™W
(xm™W
º 15)°
34.triangle
m™A
=
x°triangle
35.triangle.
m™R
= x° =
m™W
15)° ?
?
?
23.
An
is
is
an
isosceles
triangle.
!!!!!
!!!!!
!!!
!!!
24.
An
interior
angle
of
a
triangle
and
one
of
its
adjacent
exterior
angles
m™B of
= a2x°
= 7x° m™S
= (2x º
165)°
24. An
interior
triangle
and
one
ofm™S
its adjacent
exterior
m™B
= 2x°angle
= 7x°
m™Y
= (2xm™Y
º? 165)°
m™Bm™S
= 2x°
= angles
7x°
m™Y
= (2x º 165)°
are !!!!!
supplementary.
!!! An
interior
24.angle
An interior
of a triangle
angle of
anda one
triangle
of itsand
adjacent
one ofexterior
its adjacent
angles
exterior angles
? ?24.
°
m™C
= (2x m™C
+ 15)°
m™T = x° m™Tm™Z
are
supplementary.
!!!!!=
!!!(2x
m™C
+ 15)°
m™T
=+
x° 15)°
= (2x
= x°= 90°m™Z = 90° m™Z = 90°
?!!!
?!!! supplementary.
are
are !!!!!
supplementary.
?!!! complementary.
25.each
The
acute
angles
of
a right
triangle
!!!!!
Find
the
value
of!!!!!
x.of
Find
measure.
?!!!
25.
The
acute
angles
a right
triangle
areare
complementary.
!!!!!
5) 18.
4)
16.
17.
?!!!
?!!!angle
25.
The
acute
25.
angles
The
acute
of
a
right
angles
triangle
of
a
right
are angle.
triangle
are !!!!!
complementary.
complementary.
?
26.
A
triangle
has
a
right
angle
and
an
obtuse
xy E
!!!!!
!!!!!
!!!
3 shown.
XTERIOR
ANGLES
Find
theof
measure
of
the
exterior
?
xy A
26.
triangle
has
a
right
angle
and
an
obtuse
angle.
x
!!!!!
!!!
y
E
XTERIOR
A
NGLES
Find
the
measure
the
exterior
angle
shown.
E
XTERIOR
A
NGLES
Find
the
measure
of
the
exterior
angle shown.
4)
58°
3.3)
m∠1
?!!!
?!!!angle
1
26. A triangle
26. A
triangle
has a right
has aand
right
anangle
obtuse
and
angle.
an obtuse
angle.
!!!!!
85°
2
IDENTIFYING
PARTS OF!!!!!
TRIANGLES
Refer
to the triangles
in Exercises
16–21.
37.
38.
39.
I37.
DENTIFYING PARTS OF37.
TRIANGLES
Refer to the triangles
38.
38. 39. in Exercises 16–21.
! 137°
85° x39.
20°
4. m∠2
x ! 16–21.
IDENTIFYING
IDENTIFYING
Pthe
ARTS
OF TP
RIANGLES
ARTS
OF right
TRefer
RIANGLES
to the Refer
triangles
tox !the
in Exercises
triangles
in
16–21.
Exercises
35°
27. Identify
the legs and
hypotenuse
of any
triangles.
38!
27. Identify 20°
the legs and the hypotenuse
50°
? triangles.38!
38! of any right
39° triangles.
27.the
Identify
27.the
legs
Identify
andofthe
hypotenuse
legs
and thetriangles.
of
hypotenuse
any right
of any
right triangles.
(2x
8)!the
5. m∠3
28. Identify
legs"and
base
any
isosceles
Which
50°
(2x " 8)!
(2x of
" 8)!
?isosceles
28.
the legs and the base
any isosceles triangles. Which isosceles
130°Identify
? 28.
triangle
has
a base
that
is
also
the
hypotenuse
of
a
right
triangle?
(10x
#
9)!
(2xWhich
" 21)! isosceles
Identify
the
28.
legs
Identify
and
the
base
legs
and
of
any
the
isosceles
base
of
any
triangles.
isosceles
Which
triangles.
isosceles
31! the hypotenuse
! is also
(10x # 9)!
" 21)!
# 9)!
(2x " 21)!
triangle has a base xthat
of a right triangle?(10x (2x
31!
x!
31!
x!
130°
?base that
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has#
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also
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theof
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a right triangle?
of a right triangle?
102°
?
xy USING ALGEBRA
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Use
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Æ
Æ
y
is a leg of40.
isosceles
triangle.
xan
xLGEBRA
y U
yright
Aright
AUse
LGEBRA
SING
USING
Use
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graph.
UseThe
the segment
graph.
The
ABsegment
AB
TECHNOLOGY
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40.
ECHNOLOGY
Use
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Sum
40.
T
ECHNOLOGY
Use
geometry
software
toy demonstrate
the Triangle Sum
is
a
leg
of
an
is
isosceles
a
leg
of
an
right
isosceles
triangle.
right
triangle.
C(?,
?)
6)
19.
each
numbered
Theorem
or theC.Exterior
Angle
Theorem. Describe your procedure. C (?, ?)
29. Find
FindTheorem
the coordinates
ofangle.
point
Copy
the
graph
or
the
Exterior
Angle
Theorem.
Describe
your
procedure.
Theorem
or
the
Exterior
Angle
Theorem.
Describe
your
procedure. C (?, ?)
29. Find the coordinates of point C. Copy the graph
2°
FINDING
angles.
100°
? ANGLE MEASURES Find the measure of the numbered
FINDING ANGLE
FINDING
MEASURES
ANGLE M
Find
EASURES
the measure
Find the
of measure
the numbered
of theangles.
numbered
NT HELP
STUDENT HELP
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31.
32.
33.
10.
m∠5
102°
100°
?
35°
1 33.
Pb site E31.
RNET
32.
1
HOMEWORK HELP HOMEWORK
HELP
1
31.
31.
32.
32.
33.
1
35°33.
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site
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1
Visit
Visit our Web site
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3.
42!
with Exs.
for31–33.
help with Exs. 31–33.
1
1
3
42!
42!
3
2
95!
95!
42!
2
40!
340! 2
95!
56!
56!
1
50! 3
50!
1 2
40!
1 2
45!
3
245!
40!
45!
95!
8)
7)xy USING ALGEBRA The variable expressions represent
8)the 1angle
155° B
58°angle
xy U
Find
each
SING measure.
A
The
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155°
xof
xy Find
measures
a triangle.
the measure
of each
angle.the
Then
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the
yLGEBRA
20°
56!
50!
1 45!
2
3
50!
1 2
3
64° C
USING ALGEBRA
USINGThe
ALGEBRA
variableThe
expressions
variable expressions
represent60°
the
represent
angle the angle
measures
of aits
triangle.
Find the measure of each angle. Then classify the
triangle by
angles.
measures
a triangle.ofFind
a triangle.
the measure
Find the
of measure
each angle.
of each
Thenangle.
classify
Then
the 60°
classify the
? ofmeasures
triangle
its angles.
12.
m∠1 by triangle
2
by
its
triangle
angles.
by
its
angles.
30°
A
D
20.
34. m™A = x°
35. m™R =21.
x°
36. m™W?= (x º 15)° 22.
m™A =34.
x° m™A = 34.
35.
m™R
=
x°
36.
m™W
(x º
15)°=36.
13.34.
m∠2
?
x° m™A m™S
= x° =
35.7x°
m™R = 35.
x° m™R
= x°==
36.
m™W
(x º
m™W
15)°
= (x º 15)°
m™B = 2x°
m™Y
(2x
º 165)°
20°
?
°
356!
angles.
m™B = 2x°m™B =20°
m™S
= 7x°m™S = 7x° m™S
m™Y
= (2x m™Y
º 165)°
= 2x°
=
7x°
= (2x º
m™Y
165)°
= (2x º 165)°
m™C = (2x + 15)°2x° m™B m™T
= x°
m™Z
= 90°
m™C = (2xm™C
+ 15)°
m™T
=
x°
m™Z
=
90°
= (2x m™C
+ 15)°= (2x + 15)°
m™T = x° m™T = x°
m™Z = 90° m™Z = 90°
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6) the graph
6.5)
m∠1
and sketch
¤ABC.
29. Find
the 29.
coordinates
Find the of
coordinates
point C. Copy
of point
the C.
graph
Copy
and sketch
¤ABC.
and sketch ¤ABC.
and sketch ¤ABC.
5
4.1 Triangles
A (2, 2)?4.1and
B (5, Angles
2)199 and199
7. m∠4
30. Find the coordinates of a point D that forms
a Triangles
4.1
and
Angles
199
2
A(2,Angles
2)
B(5, Triangles
2) 7)
30. Find137°
the coordinates of a point D that formsÆ
a
A?(2, 2)
(5, 2)
B (5, 2)
different
right
triangle
with
leg
AB
. a forms
Æ
30.isosceles
Find the 30.
coordinates
Find
the of
coordinates
a point
D of
that
point Da that forms a A (2, 2) x B70°
118°
3
4
different isosceles right triangle with leg AB.
Æ
Æ
8. m∠3
Include a sketch
with
your
answer.
x
different
isosceles
different
right
isosceles
triangleright
withtriangle
leg AB. with
leg AB
.
6
1
36°
65°
Include a sketch with your answer.
x
x
?
Include
a
sketch
Include
with
a
your
sketch
answer.
with
your
answer.
9. m∠2
68°
82°
FINDING ANGLE MEASURES Find the measure of the numbered
angles.
30°
xy EXTERIOR ANGLES
14. CONSTRUCTION
TheFind
diagram
shows of
anthe exterior angle shown.
the measure
xy EXTERIOR
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37.
38.
39.
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37.
38.
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37.
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(2x " 8)!
x!
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Chapter
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40.
37.
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31!
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38.
38.
38!
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38!
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31!
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40.
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Use
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-1Worksheet by Kuta Software LLC
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-1-
4.1 Triangles and Angles
4.1 Triangles and Angles
199
199
Worksheet by Kuta Software LLC
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23. An isosceles triangle has ________________________ congruent sides.
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