Question

triangle klm is similar to triangle tlv.which statement about the triangles must be true?a \\( \frac { k l } { l m } = \frac { l v } { t l } \\)b \\( \frac { m l } { m k } = \frac { v l } { v t } \\)c angle k is congruent to angle v.d angle t is congruent to angle m.

Explanation:

Step1: Recall the properties of similar triangles

Similar triangles have corresponding angles congruent and corresponding sides in proportion.

Step2: Analyze each option

• Option A: For similar triangles \( \triangle KLM\sim\triangle TLV\), the proportion should be \( \frac{KL}{TL}=\frac{LM}{LV}\) (corresponding sides), not \( \frac{KL}{LM}=\frac{LV}{TL}\).
• Option B: Since \( \triangle KLM\sim\triangle TLV\), \( \frac{ML}{VL}=\frac{MK}{VT}\) (corresponding sides), so \( \frac{ML}{MK}=\frac{VL}{VT}\) (by cross - multiplication property of proportions).
• Option C: In similar triangles \( \triangle KLM\sim\triangle TLV\), \( \angle K\) corresponds to \( \angle T\), not \( \angle V\).
• Option D: In similar triangles \( \triangle KLM\sim\triangle TLV\), \( \angle T\) corresponds to \( \angle K\), not \( \angle M\).

Answer:

B. \( \frac{ML}{MK}=\frac{VL}{VT}\)