Question

problem 21: select the converse of this statement, and determine whether it is true or false. if all three corresponding angles and all three corresponding sides of two triangles are congruent, then the triangles are congruent.

Explanation:

Step1: Recall converse definition

The converse of a conditional statement "If p, then q" is "If q, then p". Here, p is "all three corresponding angles and all three corresponding sides of two triangles are congruent" and q is "the triangles are congruent".

Step2: Determine truth - value

By the definition of congruent triangles (two triangles are congruent if and only if their corresponding parts are congruent), the converse is true.

Answer:

Converse: If two triangles are congruent, then all three corresponding angles and all three corresponding sides of the two triangles are congruent. True.