Question

1. determine if the triangles below are congruent. if yes, state which method.

a)
b)
c)
d)

Explanation:

Step1: Recall congruence criteria

Congruent triangles have equal - corresponding sides and angles. Common congruence methods are SAS (Side - Angle - Side), SSS (Side - Side - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - triangles).

Step2: Analyze part a

In part a, we have two triangles with two pairs of corresponding sides equal and the included angles equal. So, by SAS (Side - Angle - Side) criterion, the triangles are congruent.

Step3: Analyze part b

In part b, we have three pairs of corresponding sides equal. So, by SSS (Side - Side - Side) criterion, the triangles are congruent.

Step4: Analyze part c

In part c, we have two pairs of corresponding sides equal and the vertical angles (which are equal) as the included angles. So, by SAS (Side - Angle - Side) criterion, the triangles are congruent.

Step5: Analyze part d

In part d, we have a right - triangle situation. The hypotenuse and one leg of one right - triangle are equal to the hypotenuse and one leg of the other right - triangle. So, by HL (Hypotenuse - Leg) criterion, the triangles are congruent.

Answer:

a) Yes, by SAS.
b) Yes, by SSS.
c) Yes, by SAS.
d) Yes, by HL.