Question

question 9 of 10
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 Given Congruences

We know \( \triangle ABC \cong \triangle DEF \) and \( \triangle MNO \cong \triangle PQR \), but \( \triangle DEF \) and \( \triangle MNO \) aren't stated to be congruent. So we can't use transitivity to conclude \( \triangle ABC \cong \triangle PQR \).

Answer:

B. False