Chapter 7.5, Problem 4CE

To determine

To show: Whether the similarity of triangles can be proved. If so, to give the suitable theorem or postulate.

Answer to Problem 4CE

Thetriangles are not similar.

Explanation of Solution

Given:

The triangles are shown below:

  

Calculation:

In triangle WXV and ZXY,

Consider the ratio of sides as follows:

  $$

  $\begin{array}{l}\frac{WX}{ZX}=\frac{12}{9}=\frac{4}{3}\\ \frac{WV}{ZY}=\frac{8}{6}=\frac{4}{3}\end{array}$

And angle WXV and ZXY are vertical opposite angles and are equal.

  $\angle WXV=\angle ZXY\left(\text{Vertical}\text{opposite}\text{angles}\right)$

The ratios of sides and one angle are equal but no rule is applicable of similarity of triangle because they neither come under AA nor SAS nor SSS.

Hence, thetriangles are not similar.