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Geometry 1A
Name ________________
Homework
4.1
∆LMC ≅ ∆BJK . Complete the congruence statements.
1. LC ≅ _____
2. JB ≅ _____
3. ∠K ≅ _____
4. ∆CML ≅ _____
M
L
J
C
K
B
5. ∠M ≅ _____
6. The last piece of the jigsaw puzzle
must be put into place. Name the
corners of the piece that
correspond to the corners of A, B,
C, and D.
7. POLY ≅ SIDE . List four pairs of congruent angles.
In the two lifeguard chairs, ABCD ≅ FGHI . Find the measure of the angle or the length
of the side.
8. HI = ______
9. m∠ADC =
_______
36 in
10. BC = ______
_______
11. m∠IFG =
33 in
o
o
103
105
54 in
o
77
34 in
o
75
12. Can you conclude the figures are congruent? Justify your answer.
V
S
7
4
8
P
5
6
T
7
Q
U
13. Can you conclude the figures are congruent? Justify your answer.
E
F
J
120o
4
4
60o
H
K
G
14. Use the information given in the diagram. Tell why each statement is true.
a. AB DC
b. ∠CAB ≅ ∠ACD
c. ∠B ≅ ∠D
d. ∠BCA ≅ ∠DAC
e. AC ≅ AC
f. AB ≅ DC ; BC ≅ AD
g. ∆ABC ≅ ∆CDA
∆ACD ≅ ∆ACB
15. Find the value of x.
D
A
6xo
30o
C
B
16. ∆ABC ≅ ∆DEF . Find the value of the variable and the measure of each angle.
m∠B =
21o
( 3y ) , m∠E =
o
17. ∆ABC ≅ ∆DEF . Find the value of the variable and the measure of each side
length.
AC
= 7a + 5 , DF
= 5a + 9
Write the congruence statement for each pair of triangles.
C
18.
19. E is the midpoint of CD

20. TK bisects ∠PTR
D
P
B
X
Y
K
T
E
R
H
B
A
C
J
∆YJB ≅ ______
∆AED ≅ ______
∆TRK ≅ ______
Answers
1. BK
2. ML
3. ∠C
4. ∆KJB
5. ∆JBK
6. E, K, G, N
7. ∠P ≅ ∠S ; ∠O ≅ ∠I ; ∠L ≅ ∠D ; ∠Y ≅ ∠E
8. 54 in.
9. 77o
10. 34 in.
11. 103o
12. No; the corresponding sides are not congruent
13. Yes; all corresponding sides and angles are congruent
14. a. Given
b. If lines are parallel, then alternate interior angles are congruent
c. Given
d. If two angles of one triangle are congruent to two angles of another
triangle, then the third pair of angles are congruent.
e. Reflexive Property of Congruence
f. Given
g. Definition of congruent triangles
15. 5
16. y = 7, m∠B = m∠E = 21o
17. a = 2, AC = DF = 19
18. ∆YJB ≅ ∆HCX
19. ∆AED ≅ ∆BEC
20. ∆TRK ≅ ∆TPK