Chapter 8.3, Problem 1PSA

To determine

To prove : The similarity of $\Delta ABC$ with respect to $\Delta DEF$ .

Explanation of Solution

Given information : Here, we have given that $\angle A\cong \angle D$ and $\angle 2\cong \angle 4$

Proof: As, $\angle 1+\angle 2=180°$ and $\angle 3+\angle 4=180°$ (Linear Pair Angles)

  $\Rightarrow \angle 2=180°-\angle 1$ and $\angle 4=180°-\angle 3$

Now, as $\angle 2\cong \angle 4$ ,

  $\begin{array}{l}\Rightarrow 180°-\angle 1\cong 180°-\angle 3\\ \Rightarrow \angle 1\cong \angle 3\end{array}$

Now, In $\Delta ABC$ and $\Delta DEF$

  $\angle A\cong \angle D$ (Given)

  $\angle 1\cong \angle 3$ (Proved above)

  $\Rightarrow \Delta ABC\sim \Delta DEF$ (By AA Similarity Rule)