Chapter 2, Problem 10RP

To determine

To Prove: The congruency of the $\angle HGF$ with respect to $\angle JFG$

Explanation of Solution

Given information: $\angle EGF\cong \angle EFG$ and $\angle EGH\cong \angle EFJ$ is provided in the question which will help to find the solution.

Proof: Here, $\angle EGF\cong \angle EFG$ ……….. $\left(1\right)$

and, $\angle EGH\cong \angle EFJ$ ………...... $\left(2\right)$

So that, from $\left(1\right)$

  $EF=EG$ (Opposite sides of equal angles are equal)

and, from $\left(2\right)$

  $EH=EJ$ (Opposite sides of equal angles are equal)

So that, $EF=EG$

  $EH+HF=EJ+JG$ ( $\because EH=EJ$ )

  $EJ+HF=EJ+JG$

  $HF=JG$

Hence, $\angle HGF\cong \angle JFG$ (Angle opposite to equal sides are equal)