Chapter 8.4, Problem 3PSA

To determine

To prove : The equality of $\frac{CD}{FG}$ with respect to $\frac{DE}{EG}$ .

Explanation of Solution

Given information : Here, we have given that $\angle D\cong \angle G$

Proof: In $\Delta DEC$ and $\Delta GEF$ ,

  $\angle D\cong \angle G$ (Given)

  $\angle DEC\cong \angle GEF$ (Vertically Opposite Angles)

  $\Rightarrow \Delta DEC\sim \Delta GEF$ (By AA Similarity Rule)

  $\Rightarrow \frac{CD}{FG}=\frac{DE}{EG}$ (Corresponding sides of similar triangles are equal in ratio)