Question

consider triangles pqr, mno, and stu, which have resulted from rotating, reflecting, and translating triangle xyz. use the criteria for triangle congruence to complete the statements. triangle xyz is congruent to triangle pqr by. triangle xyz is congruent to triangle mno by. triangle xyz is congruent to triangle stu by.

Explanation:

Step1: Analyze triangle XYZ and PQR

In triangle XYZ and PQR, we have a right - angle, a side adjacent to the right - angle, and an angle. This is the AAS (Angle - Angle - Side) congruence criterion.

Step2: Analyze triangle XYZ and MNO

For triangle XYZ and MNO, we can match the sides. The sides are in proportion and we can use the SSS (Side - Side - Side) congruence criterion.

Step3: Analyze triangle XYZ and STU

In triangle XYZ and STU, we have a right - angle, a side, and another side. This is the SAS (Side - Angle - Side) congruence criterion.

Answer:

Triangle XYZ is congruent to triangle PQR by AAS.
Triangle XYZ is congruent to triangle MNO by SSS.
Triangle XYZ is congruent to triangle STU by SAS.