Download Review for Mastery 8-3

Name
LESSON
Date
Class
Review for Mastery
8-3 Angle Relationships
Vertical Angles
c
a d
b
!a and !b, !c and !d
are pairs of vertical angles.
Intersecting lines form two pairs of vertical angles.
When parallel lines are cut by a transversal,
8 angles are formed, 4 acute and 4 obtuse.
120° 60°
60° 120°
The acute angles are all congruent.
120° 60°
60° 120°
The obtuse angles are all congruent.
Any acute angle is supplementary to
any obtuse angle.
In each diagram, parallel lines are cut by a transversal. Name
the angles that are congruent to the indicated angle.
2.
3.
1 2
4 3
c ba
d
5 6
8 7
The angles congruent
to !1 are:
z
wy x
e f g
h
The angles congruent
to !a are:
5.
150°
rs
t
The angles congruent
to !z are:
In each diagram, parallel lines are cut by a transversal and
the measure of one angle is given. Write the measures of
the remaining angles on the diagram.
4.
v
25°
1.
6.
135°
150°
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
24
Holt Mathematics
Name
LESSON
Date
Class
Practice C
8-3 Angle Relationships
In the figure, !1 and !3 are vertical angles.
1. If m!1 ! 123°, find m!3.
2
2. If m!1 " m!2 ! 180° and
m!2 ! 40°, find m!3.
1 3
4
In the figure, line a ! line b.
3. Name all angles congruent to !1.
c
2
4. Name all angles congruent to !2.
4
5. Name three pairs of supplementary angles.
3
6
5
1
8
7
a
b
6. If m!2 is 26°, what is the m!6?
7. If m!7 is 131°, what is the m!8?
8. If m!4 is 57°, what is the m!5?
9. If m!3 is 127°, what is the m!8?
10. If m!5 is 100°, what is the m!2?
11. If m!1 is 46°, what is the m!3?
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
23
Holt Mathematics
Name
LESSON
Date
Class
Review for Mastery
8-4 Triangles
Acute Triangle
Right Triangle
Obtuse Triangle
1 right angle
3 acute angles
1 obtuse angle
Triangle Sum Theorem: The sum of the measures
of the three interior angles of any triangle is 180°.
C
c°
In the diagram: m!A ! m!B ! m!C " 180°
A
a°
b°
B
a° ! b° ! c° " 180°
Complete to find the measure of the unknown angle.
1.
2.
C
x°
A 58°
K
32°
42°
B
J
m!A ! m!B ! m!C " 180°
!
x ° 90°
L
m!J ! m!K ! m!L " 180°
! x° "
x° !
! x° "
x° !
!
"
"
x° "
3.
x° "
4.
X
x°
Y
35°
35°
U
x°
20°
V
Z
m!X ! m!Y ! m!Z " 180°
m!U ! m!V ! m!W " 180°
x° "
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
W
122°
x° "
32
Holt Mathematics
Name
Date
LESSON
Class
Practice C
8-4 Triangles
Find the value of each variable.
1.
62°
4.
2.
x°
3.
44°
n°
x°
w°
w°
118°
5.
t°
6.
59°
m°
t°
t°
2x °
x°
64°
7. The measure of the second angle in a triangle is four more than
the measure of the first angle and the measure of the third angle
is eight more than twice the measure of the first angle. Find the
measure of each angle.
Describe each statement as always, sometimes, or never true.
8. An obtuse triangle is a scalene triangle.
9. A scalene triangle is an isosceles triangle.
10. A right triangle is an isosceles triangle.
11. In the figure, R
!T
! is a diagonal of
rectangle QRST. Find the length of !
QT
!.
Q
R
25 ft
T
24 ft
S