Question

question 4 of 10
which statement is an example of the transitive property of congruence?

a. $\triangle klm \cong \triangle klm$

b. if $\triangle klm \cong \triangle pqr$, then $\triangle pqr \cong \triangle stu$

c. if $\triangle klm \cong \triangle pqr$ and $\triangle pqr \cong \triangle stu$, then $\triangle klm \cong \triangle stu$

d. if $\triangle klm \cong \triangle pqr$, then $\triangle pqr \cong \triangle klm$

Explanation:

The transitive property of congruence states that if figure A is congruent to figure B, and figure B is congruent to figure C, then figure A is congruent to figure C. Let's analyze each option:

• Option A: This shows a triangle is congruent to itself, which is the reflexive property, not transitive.
• Option B: There's no logical connection given to show the transitive property; it just states two congruences without the proper relationship.
• Option C: It follows the transitive property structure: If \( \triangle KLM \cong \triangle PQR \) (A ≅ B) and \( \triangle PQR \cong \triangle STU \) (B ≅ C), then \( \triangle KLM \cong \triangle STU \) (A ≅ C).
• Option D: This is the symmetric property of congruence (if A ≅ B, then B ≅ A), not transitive.

Answer:

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