Chapter 7.5, Problem 8CE

To determine

To prove: $\Delta RST\sim \Delta XYZ$ by the SAS similarity theorem.

Answer to Problem 8CE

Theratios of $\frac{RS}{XY}$ and $\frac{RT}{XZ}$ must be equal to prove $\Delta RST\sim \Delta XYZ$ by SAS similarity theorem.

Explanation of Solution

Given:

The triangles are similar by theorem SAS.

  $\angle R=\angle X\left(\text{Given}\right)$

Calculation:

SAS theorem for similarity states that the ratios of two sides of one triangle to the corresponding triangle’s two side must be equal. Angle between equal ratios sides of both the triangle must be equal.

In triangle RST and XYZ,

  $\angle R=\angle X\left(\text{Given}\right)$

Ratios of the sides with end R and X must be equal.

Consider the ratios of sides as follows:

  $$

  $\frac{RS}{XY}=\frac{RT}{XZ}$

Hence, theratios of $\frac{RS}{XY}$ and $\frac{RT}{XZ}$ must be equal to prove $\Delta RST\sim \Delta XYZ$ by SAS similarity theorem.