Question

3 if \\( \triangle k l m \sim \triangle r s t \\), which of the following statements is not true?
(a) \\( \angle m \cong \angle t \\)
(b) \\( \angle l \cong \angle s \\)
(c) \\( \angle k \cong \angle t \\)
(d) \\( \angle k \cong \angle r \\)

Explanation:

When two triangles are similar ($\triangle KLM\sim\triangle RST$), their corresponding angles are congruent. The order of the letters in the similarity statement gives the correspondence. So, $\angle K$ corresponds to $\angle R$, $\angle L$ corresponds to $\angle S$, and $\angle M$ corresponds to $\angle T$.

• Option A: $\angle M$ and $\angle T$ are corresponding angles, so $\angle M\cong\angle T$ (True).
• Option B: $\angle L$ and $\angle S$ are corresponding angles, so $\angle L\cong\angle S$ (True).
• Option C: $\angle K$ corresponds to $\angle R$, not $\angle T$. So $\angle K\cong\angle T$ is False.
• Option D: $\angle K$ and $\angle R$ are corresponding angles, so $\angle K\cong\angle R$ (True).

Answer:

C. $\angle K\cong\angle T$