Question

determine if the two triangles are congruent. if they are, state how you know. there are 2 problems that are not congruent. 7) 8) 9) 10)

Explanation:

Step1: Recall congruence criteria

Congruence of triangles can be determined by SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - triangles).

Step2: Analyze problem 7

There are two pairs of angles marked equal. But we don't have enough information about the sides. So, the triangles are not congruent.

Step3: Analyze problem 8

We have two pairs of sides marked equal and the included angles marked equal. By SAS (Side - Angle - Side) criterion, the triangles are congruent.

Step4: Analyze problem 9

We have one pair of sides marked equal and one pair of angles marked equal. Not enough information to prove congruence. So, the triangles are not congruent.

Step5: Analyze problem 10

We have two pairs of angles marked equal and a pair of non - included sides marked equal. By AAS (Angle - Angle - Side) criterion, the triangles are congruent.

Answer:

1. Not congruent.
2. Congruent by SAS.
3. Not congruent.
4. Congruent by AAS.