Question

For Each pair of triangles, determine if they can be proven congruent. if yes, state the congruence criteria and write a congruence statement. If not, write not enough information.

Answer 1

In order to determine if two triangles can be proven congruent, we need to examine the given information and apply congruence criteria. Here are the steps you can follow:

1. Compare the corresponding sides of the triangles: Check if the lengths of the sides are equal. If all three sides of one triangle are equal to the corresponding three sides of the other triangle, the triangles are congruent. This congruence criterion is known as Side-Side-Side (SSS).

2. Compare the corresponding angles of the triangles: Check if the measures of the angles are equal. If all three angles of one triangle are equal to the corresponding three angles of the other triangle, the triangles are congruent. This congruence criterion is known as Angle-Angle-Angle (AAA).

3. Compare the lengths of two sides and the measure of the included angle: If the two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of the other triangle, the triangles are congruent. This congruence criterion is known as Side-Angle-Side (SAS).

4. Compare the lengths of two angles and the length of the included side: If the two angles and the included side of one triangle are equal to the corresponding two angles and included side of the other triangle, the triangles are congruent. This congruence criterion is known as Angle-Side-Angle (ASA).

Explanation: