Chapter 8.3, Problem 2PSA

To determine

To prove : The similarity of $\Delta GHM$ with respect to $\Delta GJK$ .

Explanation of Solution

Given information : Here, we have given a $\Delta GJK$ , with point H on $\overline{GJ}$ and a point M on $\overline{GK}$ and $\overline{HM}\parallel \overline{GK}$ .

  

Proof: As, $\overline{HM}\parallel \overline{GK}$ ,

  $\Rightarrow \angle GHM\cong \angle GJK$ and $\angle GMH\cong \angle GKJ$ (Corresponding Angles)

Now, In $\Delta GHM$ and $\Delta GJK$

  $\angle GHM\cong \angle GJK$ (Proved above)

  $\angle GMH\cong \angle GKJ$ (Proved above)

  $\Rightarrow \Delta GHM\sim \Delta GJK$ (By AA Similarity Rule)