Question

match the congruence theorem that describes how the two triangles are congruent.

Explanation:

Step1: Analyze first - pair

The first pair of triangles has three pairs of equal sides (4 = 4, 5 = 5, 7 = 7). By the Side - Side - Side (SSS) congruence theorem, if the three sides of one triangle are equal to the three corresponding sides of another triangle, the two triangles are congruent.

Step2: Analyze second - pair

The second pair of triangles has two pairs of equal sides (3.6 = 3.6, 7.1 = 7.1) and the included angle between them is equal (49° = 49°). By the Side - Angle - Side (SAS) congruence theorem, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the two triangles are congruent.

Step3: Analyze third - pair

The third pair of triangles has two pairs of equal angles (124° = 124°, 23° = 23°) and the included side between them is equal (8.9 = 8.9). By the Angle - Side - Angle (ASA) congruence theorem, if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the two triangles are congruent.

Step4: Analyze fourth - pair

The fourth pair of triangles has two pairs of equal angles (76° = 76°, 42° = 42°) and a pair of non - included equal sides (15 = 15). By the Angle - Angle - Side (AAS) congruence theorem, if two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, the two triangles are congruent.

Answer:

First pair: SSS
Second pair: SAS
Third pair: ASA
Fourth pair: AAS