Chapter 7, Problem 15CR

To determine

You would first use similar triangles to show that $\frac{RS}{?}=\frac{?}{?}$ to prove $RS\cdot UV=RT\cdot UH$ .

Answer to Problem 15CR

  $\frac{RS}{UH}=\frac{RT}{UV}$

Explanation of Solution

Given:

You want to prove $RS\cdot UV=RT\cdot UH$

Calculation:

If we want to prove $RS\cdot UV=RT\cdot UH$ , we will first find the ratio that after cross multiplying gives this result. It is more convenient since we can prove the ratio by showing two triangles similar. So,

Let one triangle be RST and the other one be UVH.

  $\begin{array}{l}RS\cdot UV=RT\cdot UH\\ \Rightarrow \frac{RS\cdot UV}{UV\cdot UH}=\frac{RT\cdot UH}{UV\cdot UH}\mathrm{...............}[\text{divide each side by }UV\cdot UH]\\ \Rightarrow \frac{RS}{UH}=\frac{RT}{UV}\end{array}$

So, first we need to show $\frac{RS}{UH}=\frac{RT}{UV}$ by proving $\Delta RST\sim \Delta UVH$ .