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

10th grade (Year 11 in England) · 16 questions · Common Core: HSG.CO.B.8, HSG.SRT.B.5 · England: GCSE Foundation Geometry, GCSE Higher Geometry

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1
Question 1
Triangles ABC and DEF have: AB = DE, BC = EF, CA = FD. Which test proves they are congruent?
- A. ASA
- B. SAS
- C. Not enough to prove congruence
- D. SSS
2
Question 2
Triangles GHI and JKL have GH = JK and HI = KL. Which extra fact would prove them congruent by SSS?
- A. ∠G = ∠J
- B. ∠H = ∠K
- C. GH = KL
- D. IG = LJ
3
Question 3
Triangles ABC and DEF have: ∠A = ∠D, ∠B = ∠E, ∠C = ∠F. Which test proves they are congruent?
- A. Not enough to prove congruence
- B. ASA
- C. SAS
- D. AAS
4
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. CA = FD
- D. AB = DE
5
Question 5
Triangles ABC and DEF have: ∠A = ∠D, AB = DE, ∠B = ∠E. Which test proves they are congruent?
- A. ASA
- B. RHS (hypotenuse–leg)
- C. AAS
- D. SAS
6
Question 6
Triangles PQR and XYZ have PQ = XY and QR = YZ. Which extra fact would prove them congruent by SSS?
- A. PQ = YZ
- B. ∠P = ∠X
- C. ∠Q = ∠Y
- D. RP = ZX
7
Question 7
Triangles ABC and DEF have: ∠A = ∠D, ∠B = ∠E, BC = EF. Which test proves they are congruent?
- A. ASA
- B. RHS (hypotenuse–leg)
- C. AAS
- D. SSS
8
Question 8
Triangles PQR and XYZ have ∠P = ∠X and ∠Q = ∠Y. Which extra fact would prove them congruent by ASA?
- A. RP = ZX
- B. QR = YZ
- C. PQ = XY
- D. ∠R = ∠Z
9
Question 9
Triangles ABC and DEF have: ∠C = ∠F = 90°, hypotenuse AB = DE, AC = DF. Which test proves they are congruent?
- A. ASA
- B. RHS (hypotenuse–leg)
- C. SAS
- D. AAS
10
Question 10
Triangles PQR and XYZ have PQ = XY and QR = YZ. Which extra fact would prove them congruent by SSS?
- A. RP = ZX
- B. ∠Q = ∠Y
- C. ∠P = ∠X
- D. PQ = YZ
11
Question 11
Triangles ABC and DEF have: ∠A = ∠D, ∠B = ∠E, ∠C = ∠F. Which test proves they are congruent?
- A. SAS
- B. Not enough to prove congruence
- C. AAS
- D. ASA
12
Question 12
Triangles GHI and JKL have GH = JK and HI = KL. Which extra fact would prove them congruent by SSS?
- A. ∠H = ∠K
- B. ∠G = ∠J
- C. GH = KL
- D. IG = LJ
13
Question 13
Triangles ABC and DEF have: ∠A = ∠D, ∠B = ∠E, BC = EF. Which test proves they are congruent?
- A. Not enough to prove congruence
- B. SSS
- C. AAS
- D. ASA
14
Question 14
Triangles PQR and XYZ have ∠P = ∠X and ∠Q = ∠Y. Which extra fact would prove them congruent by ASA?
- A. RP = ZX
- B. PQ = XY
- C. QR = YZ
- D. ∠R = ∠Z
15
Question 15
Triangles ABC and DEF have: AB = DE, ∠B = ∠E, BC = EF. Which test proves they are congruent?
- A. SAS
- B. SSS
- C. AAS
- D. ASA
16
Question 16
Triangles ABC and DEF have AB = DE and BC = EF. Which extra fact would prove them congruent by SAS?
- A. CA = EF
- B. ∠A = ∠D
- C. ∠B = ∠E
- D. ∠C = ∠F

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