Download 4.2 Practice with Examples

LESSON
4.2
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 202–210
GOAL
Identify congruent figures and corresponding parts
VOCABULARY
When two geometric figures are congruent, there is a correspondence
between their angles and sides such that corresponding angles are
congruent and corresponding sides are congruent.
Theorem 4.3 Third Angles Theorem
If two angles of one triangle are congruent to two angles of another
triangle, then the third angles are also congruent.
EXAMPLE 1
Using Properties of Congruent Figures
In the diagram, ABCDE FGHIJ
a. Find the value of x.
b. Find the value of y.
B
F
(3x 4)
A
C
J
47
10
H
D
G
E
(8y 9)
I
SOLUTION
a. You know that AE FJ.
b. You know that D I.
So AE FJ.
So, mD mI.
10 3x 4
47 8y 9
x2
56 8y
Chapter 4
y7
64
Geometry
Practice Workbook with Examples
Copyright © McDougal Littell Inc.
All rights reserved.
LESSON
4.2
CONTINUED
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 202–210
Exercises for Example 1
In Exercises 1 and 2, for each pair of figures find (a) the value
of x and (b) the value of y.
1. ABC DEF
B
F
C
22
3x
9
E
A
(5y 3)
2. ABCDEF GHIJKL
C
D
G
(4x 5)
4 D
I
H
L
A
35 B
J
E
5y 2
12
F
EXAMPLE 2
K
Using the Third Angles Theorem
Find the value of x.
C
D
F
A
30
x
110
B
E
SOLUTION
Chapter 4
In the diagram, A D and B E. From the Third Angles
Theorem, you know that C F. So, mC mF.
From the Triangle Sum Theorem, mC 180 30 110 40.
mC mF
40 x
Copyright © McDougal Littell Inc.
All rights reserved.
Third Angles Theorem
Substitute.
Geometry
Practice Workbook with Examples
65
LESSON
4.2
CONTINUED
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 202–210
Exercises for Example 2
Find the value of x.
3.
x
65
4.
55
Chapter 4
5(3x 5)
66
Geometry
Practice Workbook with Examples
Copyright © McDougal Littell Inc.
All rights reserved.