Common Core HSG.CO.B.8 worksheet

Question 1

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

• A. AAS
• B. Not enough to prove congruence
• C. SSS
• D. ASA

Question 2

Two triangles are known to be congruent because both have a right angle, and the hypotenuses and one other side are equal. Which condition is this?

• A. RHS (HL)
• B. SSS
• C. SAS
• D. ASA

Question 3

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

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

Question 4

Two triangles have only two pairs of sides equal. Must they be congruent?

• A. Yes
• B. No

Question 5

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

• A. Not enough to prove congruence
• B. SAS
• C. AAS
• D. ASA

Question 6

Two triangles are known to be congruent because both have a right angle, and the hypotenuses and one other side are equal. Which condition is this?

• A. SAS
• B. RHS (HL)
• C. ASA
• D. SSS

Question 7

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

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

Question 8

Two triangles have all three angles equal (AAA). Must they be congruent?

• A. Yes
• B. No

Question 9

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. AAS

Question 10

Two triangles are known to be congruent because all three pairs of sides are equal. Which condition is this?

• A. RHS (HL)
• B. ASA
• C. SSS
• D. SAS

Question 11

Triangles PQR and XYZ have PQ = XY and QR = YZ. Which extra fact would prove them congruent by SAS?

• A. ∠P = ∠X
• B. ∠R = ∠Z
• C. RP = YZ
• D. ∠Q = ∠Y

Question 12

Two triangles have all three angles equal (AAA). Must they be congruent?

• A. Yes
• B. No

Question 13

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. ASA
• C. SSS
• D. RHS (hypotenuse–leg)

Question 14

Two triangles are known to be congruent because two angles and the side between them are equal. Which condition is this?

• A. SSS
• B. RHS (HL)
• C. ASA
• D. SAS

Question 15

Triangles KLM and STU have KL = ST and LM = TU. Which extra fact would prove them congruent by SAS?

• A. MK = TU
• B. ∠L = ∠T
• C. ∠M = ∠U
• D. ∠K = ∠S

Question 16

Two triangles have two angles and the included side equal (ASA). Must they be congruent?

• A. Yes
• B. No