Name: ________________________ Class: ___________________ Date: __________
ID: A
Congruency Items from Geo Test Bank
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
____
1. The folding chair has different settings that change the angles formed by its parts. Supposem∠2 is 26 and m∠3 is
70. Find m∠1. The diagram is not to scale.
a. 96
b. 106
c. 116
d. 86
2. In the paper airplane, ABCD ≅ EFGH, m∠B = m∠BCD = 90, and m∠BAD = 131. Find m∠GHE.
a. 131
b. 49
c. 90
d. 59
3. What other information do you need in order to prove the triangles congruent using the SAS Congruence
Postulate?
a.
b.
∠BAC ≅ ∠DAC
∠CBA ≅ ∠CDA
c.
d.
1
AC ⊥ BD
AC ≅ BD
Name: ________________________
____
____
____
ID: A
4. State whether ΔABC and ΔAED are congruent. Justify your answer.
a. yes, by either SSS or SAS
b. yes, by SSS only
c. yes, by SAS only
d. No; there is not enough information to conclude that the triangles are congruent.
5. Based on the given information, what can you conclude, and why?
Given: ∠H ≅ ∠L, HJ ≅ JL
a. ΔHIJ ≅ ΔLKJ by ASA
b. ΔHIJ ≅ ΔJLK by SAS
6. Find the values of x and y.
c.
d.
ΔHIJ ≅ ΔJLK by ASA
ΔHIJ ≅ ΔLKJ by SAS
x = 90, y = 47
x = 43, y = 47
c.
d.
x = 47, y = 43
x = 90, y = 43
a.
b.
2
Name: ________________________
ID: A
____
7. The octagon in the figure is equiangular and AB ≅ AC . Find m∠ACB.
____
a. 135
b. 45
c. 30
d. 90
8. What is the measure of a base angle of an isosceles triangle if the vertex angle measures38° and the two
congruent sides each measure 21 units?
a. 71°
b. 142°
c. 152°
d. 76°
____ 9. What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures42°?
a. 69°
b. 84°
c. 138°
d. 96°
____ 10. Find the value of x. The diagram is not to scale.
a.
x = 23
b.
x = 40
c.
3
x = 13
d.
none of these
Name: ________________________
ID: A
____ 11. Find the value of x. The diagram is not to scale.
Given: RS ≅ ST, m∠RST = 3x − 48, m∠STU = 9x
a. 19
b. 105
c. 21
d. 24
____ 12. Q is equidistant from the sides of ∠TSR. Find the value of x. The diagram is not to scale.
a.
27
b.
3
c.
15
d.
30
d.
6
____ 13. DF bisects ∠EDG. Find the value of x. The diagram is not to scale.
a.
23
42
b.
90
c.
4
30
Name: ________________________
ID: A
⎯⎯
⎯
→
____ 14. DF bisects ∠EDG. Find FG. The diagram is not to scale.
a.
15
b.
14
c.
19
d.
28
Short Answer
15. Find the measure of each interior and exterior angle. The diagram is not to scale.
16. Name a pair of triangles in the figure and state whether they are congruent by SSS, SAS, ASA, AAS, or HL.
Given: NP ≅ OM , MN ≅ PO
5
Name: ________________________
ID: A
17. Write a two-column proof to show that ΔOQR ≅ ΔMQR.
Given: NO ≅ PM, ∠1 ≅ ∠2, and OR ≅ MR
18. In the figure, ∠1 ≅ ∠2, ∠3 ≅ ∠4, and TK ≅ TL. Prove that ΔRTK ≅ ΔSTL.
Essay
19. Find the values of the variables. Show your work and explain your steps. The diagram is not to scale.
6
Name: ________________________
ID: A
20. Write a proof.
Given: BC ≅ DA, ∠1 ≅ ∠2, and CF ≅ AF
Prove: ΔCFE ≅ ΔAFE
21. Write a paragraph proof to show that ΔABC ≅ ΔDEC .
Given: AC ≅ DC and BC ≅ CE
22. Write a two-column proof.
Given: BC ≅ EC and AC ≅ DC
Prove: BA ≅ ED
23. Write a two-column proof:
Given: ∠BAC ≅ ∠DAC, ∠DCA ≅ ∠BCA
Prove: BC ≅ CD
7
Name: ________________________
ID: A
24. AC and BD are perpendicular bisectors of each other. Find BC, AE, DB, and DC. Justify your answers.
Other
25. Is there enough information to prove the two triangles congruent by AAS? If yes, write the congruence statement
and explain. If no, write not possible and tell what other information you would need.
Given: ∠B ≅ ∠D
8