Chapter 12.5, Problem 3CK

To determine

Tofind:The reason for $\frac{ED}{VO}=\frac{DB}{OB}$ in the triangles $\Delta EDB$ and $\Delta VOB$ .

Answer to Problem 3CK

The ratio of corresponding sides of triangle is equal because both triangles are similar.

Explanation of Solution

Given information:The figure is shown below:

  

Calculation:

In $\Delta EDB$ and $\Delta VOB$ , $\angle \text{B}$ is common in both triangles. So, their measure will be the same.

The measure of $\angle VOB$ and $\angle EDB$ is $90°$ . Let the angle be $c$ . It is known that the sum of interior angles of triangle is $180°$ .

The third angle of $\Delta VOB$ is:

  $180°-90°-c=90°-c$

The third angle of $\Delta EDB$ is:

  $180°-90°-c=90°-c$

As all the three angles of $\Delta EDB$ and $\Delta VOB$ are equal. So, $\Delta VOB\sim \Delta EDB$ .

By the similarity of two triangles the corresponding sides of similar triangles are equal in ratio:

  $\frac{ED}{VO}=\frac{DB}{OB}$

Therefore, the ratio of corresponding sides of triangle is equal because both triangles are similar.