Download Lesson 4.1

Name
Class
Date
Practice
4-1
Form K
Congruent Figures
Each pair of polygons is congruent. Find the measures of the numbered angles.
1. M
2.
Q
G
B
1
A
F
2
1
2
L
90; 40
D
40
N
P
R
C
95
45
60
150
H
I
95; 60
Use the diagram at the right for Exercises 3–7. kABC O kXYZ.
Complete the congruence statements.
u
3. AB > XY
X
A
B Y
Z
C
To start, use the congruence statement to identify
the points that correspond to A and B.
u
u
A corresponds to X . B corresponds to Y .
u
u
lY
7. /B > u
5. /Z > lC
4. ZY > CB
z
6. /BAC > lYXZ
z
FOUR O MANY . List each of the following.
8. four pairs of congruent angles lF O lM; lO O lA; lU O lN; lR O lY
9. four pairs of congruent sides FO O MA; OU O AN; UR O NY ; RF O YM
For Exercises 10 and 11, can you conclude that the figures are congruent?
Justify your answers.
10. nSRT and nPRQ
11. nABC and nFGH
S
B
A
R
H
Q
T
P
No; lSRT O lPRQ because vert. ' are O,
and lRST O lRPQ by Third Angles Thm.,
but none of the sides are necessarily
congruent.
C
G
Yes; lBAC O lGFH by Third Angles
Thm. Therefore, kABC O kFGH by
the def. of O triangles.
Prentice Hall Foundations Geometry • Teaching Resources
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F
Name
Class
Date
Practice (continued)
4-1
Form K
Congruent Figures
E
12. Given: AD and BE bisect each other.
A
AB > DE; /A > /D
Prove: nACB > nDCE
C
Statements
B
Reasons
1) AD and BE bisect each other .
AB > DE, /A > /D
1) Given
2) AC > CD, BC > CE
2) 9 Definition of bisect
3) /ACB > /DCE
3) 9 Vertical angles are O.
4) /B > /E
4) 9 Third Angles Theorem
5) nACB > nDCE
5) 9 Definition of O Triangles
13. If nABC > nJKL, which of the following must be a
correct congruence statement? C
A
J
B
/A > /L
/B > /K
AB > JL
nBAC > nLKJ
D
K
L
C
14. Reasoning A student says she can use the information in the figure
B
C
to prove nACB > nACD. Is she correct? Explain.
No; explanations may vary. Sample: Corresponding
parts are not congruent. The figure can be used to
prove kACB O kCAD.
A
D
Algebra Find the values of the variables.
15. nXYZ > nFED 3; 15
Z
30
X 9 in. Y
16. nABD > nCDB 15
D
B
(5x)
(2y)
A
75
C
D
E 3x in. F
Algebra kFGH O kQRS. Find the measures of the given angles or the lengths
of the given sides.
18. GH 5 3x 2 2; RS 5 x 1 6 10; 10
17. m/F 5 x 1 24; m/Q 5 3x 36; 36
Prentice Hall Foundations Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
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