Question

if \\( \triangle k l m \cong \triangle r s t \\), which of the following proportional statements is not true
a \\( \frac{k m}{r s} \\)
b \\( \frac{k m}{r t} \\)
c \\( \frac{k l}{r s} \\)
d \\( \frac{l m}{s t} \\)

Explanation:

Step1: Recall the properties of congruent triangles

When \(\triangle KLM\cong\triangle RST\), the corresponding sides are equal. That is \(KL = RS\), \(LM=ST\), \(KM = RT\).

Step2: Analyze each option

• Option A: \(\frac{KM}{RS}\), since \(KM = RT

eq RS\) (from congruence \(KM = RT\)), this ratio is not \(1\) (assuming non - degenerate triangles where side lengths are positive).

• Option B: \(\frac{KM}{RT}\), because \(KM = RT\), \(\frac{KM}{RT}=1\).
• Option C: \(\frac{KL}{RS}\), as \(KL = RS\), \(\frac{KL}{RS}=1\).
• Option D: \(\frac{LM}{ST}\), since \(LM = ST\), \(\frac{LM}{ST}=1\).

Answer:

A. \(\frac{KM}{RS}\)