Chapter 7, Problem 5PT

To determine

To find: Whether each pair of figures is similar and also write similarity statement and scale factor.

Answer to Problem 5PT

  $\Delta XYZ\sim \Delta ABC$ by $SAS$ similarity theorem. And the scale factor is $\frac{2}{7}$ .

Explanation of Solution

Given information:

Given the figure.

  

Calculation:

When the length of the triangles are proportional to the length of two corresponding sides of another triangle and the included angles are congruent.

So, the triangles are similar by $SAS$ similarity theorem.

Given that $\angle Y$ and $\angle B$ are right angles.

Therefore,

  $\angle Y\cong \angle B$

  

The ratio of corresponding sides

  $\begin{array}{c}\frac{XY}{AB}=\frac{4}{14}\\ =\frac{2}{7}\end{array}$

And,

  $\begin{array}{c}\frac{YZ}{BC}=\frac{7}{24.5}\\ =\frac{2}{7}\end{array}$

So, $\frac{XY}{AB}=\frac{YZ}{BC}=\frac{2}{7}$

Therefore, $\Delta XYZ\sim \Delta ABC$ by $SAS$ similarity theorem and the scale factor is $\frac{2}{7}$ .