Chapter 14.4, Problem 2MRE

To determine

To find: Scale factor of $\Delta OBC$ to $\Delta ODE$ .

Answer to Problem 2MRE

Scale factor of $\Delta OBC$ to $\Delta ODE$ is $2:3$ .

Explanation of Solution

Given information :

  $\overline{ED}\left|\right|\overline{BC}\left|\right|\overline{FG}$

Concept used:

If two objects have the same shape, they are called "similar." When two figures are similar, the ratios of the lengths of their corresponding sides are equal. To determine if the triangles shown are similar, compare their corresponding sides.

As per the given problem

Following diagram is provided.

  

Given: $\overline{ED}\left|\right|\overline{BC}\left|\right|\overline{FG}$

  $\Delta OBC$ similar to $\Delta ODE$ .

  $\begin{array}{l}\frac{OB}{OD}=\frac{BC}{DE}=\frac{CO}{EO}\\ \Rightarrow \frac{BC}{DE}=\frac{2}{3}\end{array}$

Hence,

: Scale factor of $\Delta OBC$ to $\Delta ODE$ is $2:3$ .