Question

question 6 of 10
which statement is an example of the transitive property of congruence?
a. \\( \triangle k l m \cong \triangle k l m \\).
b. if \\( \triangle k l m \cong \triangle p q r \\), then \\( \triangle p q r \cong \triangle s t u \\).
c. if \\( \triangle k l m \cong \triangle p q r \\) and \\( \triangle p q r \cong \triangle s t u \\), then \\( \triangle k l m \cong \triangle s t u \\).
d. if \\( \triangle k l m \cong \triangle p q r \\), then \\( \triangle p q r \cong \triangle k l m \\).

Explanation:

Step1: Recall the transitive property of congruence

The transitive property of congruence states that if \(A\cong B\) and \(B\cong C\), then \(A\cong C\).

Step2: Analyze each option

• Option A: \(\triangle KLM\cong\triangle KLM\) is the reflexive property (a figure is congruent to itself).
• Option B: If \(\triangle KLM\cong\triangle PQR\), then \(\triangle PQR\cong\triangle STU\) does not follow any known congruence property rule as stated.
• Option C: If \(\triangle KLM\cong\triangle PQR\) and \(\triangle PQR\cong\triangle STU\), then \(\triangle KLM\cong\triangle STU\) follows the transitive property (\(A = \triangle KLM\), \(B=\triangle PQR\), \(C = \triangle STU\)).
• Option D: If \(\triangle KLM\cong\triangle PQR\), then \(\triangle PQR\cong\triangle KLM\) is the symmetric property (if \(A\cong B\), then \(B\cong A\)).

Answer:

C. If \(\triangle KLM\cong\triangle PQR\) and \(\triangle PQR\cong\triangle STU\), then \(\triangle KLM\cong\triangle STU\)