Question

question 22 of 25 given the parallelogram below, michael writes, \triangle abc is congruent to triangle cda.\ which of the following reasons allows him to write this statement? a. corresponding parts of congruent polygons theorem b. angle addition postulate c. sss property d. symmetric property

Explanation:

Step1: Recall congruence properties

In a parallelogram \(ABCD\), if we consider the relationship between \(\triangle ABC\) and \(\triangle CDA\). The symmetric property of congruence states that if \(\triangle ABC\cong\triangle CDA\), then \(\triangle CDA\cong\triangle ABC\). The corresponding - parts of congruent polygons theorem (A) is used to find equal parts after proving congruence, not to prove the initial congruence. The angle - addition postulate (B) is about adding angles and not relevant here. The SSS (side - side - side) property (C) would be used if we were showing equality of three pairs of sides to prove congruence, but the question is asking for the reason for the statement of congruence once we know the triangles are congruent. The symmetric property allows us to say that if one triangle is congruent to another, the reverse is also true.

Answer:

D. Symmetric property