Question

15
if $\triangle abc \cong \triangle def$ and $\triangle mno \cong \triangle pqr$, then $\triangle abc \cong \triangle pqr$ by the transitive property.

a. true
b. false

Explanation:

Step1: Recall Transitive Property

The transitive property of congruence states that if \( \triangle X \cong \triangle Y \) and \( \triangle Y \cong \triangle Z \), then \( \triangle X \cong \triangle Z \). Here, we have \( \triangle ABC \cong \triangle DEF \) and \( \triangle MNO \cong \triangle PQR \). There's no direct link (like \( \triangle DEF \cong \triangle MNO \)) to apply transitivity between \( \triangle ABC \) and \( \triangle PQR \).

Step2: Analyze the Given Congruences

The first congruence is between \( ABC \) and \( DEF \), the second between \( MNO \) and \( PQR \). These are two separate pairs with no common triangle to connect them for transitivity. So the statement that \( \triangle ABC \cong \triangle PQR \) by transitive property is incorrect.

Answer:

B. False