Choose the congruence test (SSS, SAS, ASA, AAS, RHS)

Question 1

Triangles ABC and DEF have: ∠C = ∠F = 90°, hypotenuse AB = DE, AC = DF. Which test proves they are congruent?

• A. RHS (hypotenuse–leg)
• B. Not enough to prove congruence
• C. SSS
• D. AAS

Question 2

Triangles ABC and DEF have AB = DE and BC = EF. Which extra fact would prove them congruent by SAS?

• A. CA = EF
• B. ∠C = ∠F
• C. ∠A = ∠D
• D. ∠B = ∠E

Question 3

Triangles ABC and DEF have: AB = DE, BC = EF, ∠A = ∠D (the angle is not between the sides). Which test proves they are congruent?

• A. Not enough to prove congruence
• B. SSS
• C. ASA
• D. RHS (hypotenuse–leg)

Question 4

Triangles ABC and DEF have ∠A = ∠D and ∠B = ∠E. Which extra fact would prove them congruent by ASA?

• A. ∠C = ∠F
• B. BC = EF
• C. AB = DE
• D. CA = FD

Question 5

Triangles ABC and DEF have: ∠A = ∠D, ∠B = ∠E, BC = EF. Which test proves they are congruent?

• A. SSS
• B. AAS
• C. SAS
• D. RHS (hypotenuse–leg)

Question 6

Triangles GHI and JKL have GH = JK and HI = KL. Which extra fact would prove them congruent by SSS?

• A. GH = KL
• B. IG = LJ
• C. ∠G = ∠J
• D. ∠H = ∠K

Question 7

Triangles ABC and DEF have: ∠C = ∠F = 90°, hypotenuse AB = DE, AC = DF. Which test proves they are congruent?

• A. Not enough to prove congruence
• B. RHS (hypotenuse–leg)
• C. ASA
• D. SAS

Question 8

Triangles PQR and XYZ have ∠P = ∠X and ∠Q = ∠Y. Which extra fact would prove them congruent by ASA?

• A. ∠R = ∠Z
• B. RP = ZX
• C. QR = YZ
• D. PQ = XY

Question 9

Triangles ABC and DEF have: ∠C = ∠F = 90°, hypotenuse AB = DE, AC = DF. Which test proves they are congruent?

• A. SAS
• B. RHS (hypotenuse–leg)
• C. SSS
• D. AAS

Question 10

Triangles ABC and DEF have AB = DE and BC = EF. Which extra fact would prove them congruent by SSS?

• A. ∠B = ∠E
• B. CA = FD
• C. AB = EF
• D. ∠A = ∠D

Question 11

Triangles ABC and DEF have: AB = DE, BC = EF, CA = FD. Which test proves they are congruent?

• A. RHS (hypotenuse–leg)
• B. Not enough to prove congruence
• C. SSS
• D. ASA

Question 12

Triangles ABC and DEF have AB = DE and BC = EF. Which extra fact would prove them congruent by SAS?

• A. CA = EF
• B. ∠C = ∠F
• C. ∠B = ∠E
• D. ∠A = ∠D

Question 13

Triangles ABC and DEF have: AB = DE, BC = EF, ∠A = ∠D (the angle is not between the sides). Which test proves they are congruent?

• A. Not enough to prove congruence
• B. AAS
• C. RHS (hypotenuse–leg)
• D. ASA

Question 14

Triangles ABC and DEF have AB = DE and BC = EF. Which extra fact would prove them congruent by SSS?

• A. CA = FD
• B. ∠B = ∠E
• C. ∠A = ∠D
• D. AB = EF

Question 15

Triangles ABC and DEF have: AB = DE, BC = EF, CA = FD. Which test proves they are congruent?

• A. SSS
• B. SAS
• C. ASA
• D. AAS

Question 16

Triangles ABC and DEF have AB = DE and BC = EF. Which extra fact would prove them congruent by SAS?

• A. ∠B = ∠E
• B. ∠C = ∠F
• C. ∠A = ∠D
• D. CA = EF