Chapter 6.7, Problem 20HP

To determine

To check: If the proportion $\frac{x}{z}=\frac{r}{t}$ , where x , r , t and z are the sides , opposite to different angles of two similar triangles XYZ and RST.

Answer to Problem 20HP

Given proportion $\frac{\text{x}}{\text{z}}=\frac{\text{r}}{\text{t}}$ is TRUE.

Explanation of Solution

Given information:

Two similar triangles XYZ and RST and x is the side opposite to angle X and z is side opposite to angle Z and similarly r is the side opposite to angle R and t is the side opposite to angle T .

Concept used:

In similar triangles, the ratio of corresponding sides is equal always. So, in given similar triangles,

  $\frac{\text{YZ}}{\text{ST}}=\frac{\text{XY}}{\text{RS}}$

And YZ is the side opposite to angle X , ST is the side opposite to angle R , XY is the side opposite to angle Z and RS is the side, opposite to angle T .

Calculation:

Based on above ratio set,

  $\frac{\text{x}}{\text{r}}=\frac{\text{z}}{\text{t}}$

On cross multiply,

  $\frac{\text{x}}{\text{z}}=\frac{\text{r}}{\text{t}}$

Based on above concept, given ratio of corresponding sides is TRUE.