Question

Prove that if a line is drawn parallel to one side of a triangle intersecting the other two sides at distinct points, then the other two sides are divided in the same ratio.

If $CB \parallel QR$ , $CA \parallel PR$ , $AQ = 12\text{ cm}$ , $AR = 20\text{ cm}$ and $PB = CQ = 15\text{ cm}$ , calculate the lengths PC and BR.

Accepted Answer

Proof of Basic Proportionality Theorem (BPT): In $	riangle PQR$, as $CA \parallel PR$, by BPT in $	riangle PQR$: $\frac{QC}{CP} = \frac{QA}{AR} \implies \frac{15}{PC} = \frac{12}{20} = \frac{3}{5} \implies PC = 25	ext{ cm}$. As $CB \parallel QR$, by BPT: $\frac{PC}{CQ} = \frac{PB}{BR} \implies \frac{25}{15} = \frac{15}{BR} \implies BR = \frac{225}{25} = 9	ext{ cm}$.

Basic Proportionality Theorem and application

Explanation

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