Question

which triangles in the diagram are congruent? triangle 1 triangle 2 triangle 3 triangle 4 a. triangle 1 and triangle 2 b. triangle 1, triangle 2, and triangle 3 c. triangle 1 and triangle 3 d. triangle 1, triangle 3, and triangle 4

Explanation:

Step1: Recall congruence criteria

Triangles are congruent if they meet SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side) or HL (Hypotenuse - Leg for right - triangles) criteria.

Step2: Analyze given triangles

In triangle 1, we have a 70° angle and two marked sides. In triangle 3, we have a 70° angle in the same relative position and the same two marked sides. By the SAS congruence criterion, triangle 1 and triangle 3 are congruent.

Answer:

D. triangle 1, triangle 3, and triangle 4