Chapter 7.2, Problem 1PSA

To determine

To prove : The congruency of $\angle G\cong \angle J$ .

Explanation of Solution

Given information : The following information has been given

  $\angle GMJ={90}^0$

  $\angle GKJ={90}^0$

Formula used : If any two angles of the triangles are congruent, then the triangles are said to be similar

Proof : We know that in triangles HGM and HJK,

  $\angle GMJ=\angle GKJ={90}^0$

  $\angle H$ is common (vertically opposite)

Thus, if any two angles of the triangles are congruent, then the triangles are said to be similar. Hence, for similar triangles, all angles are congruent

Thus, $\angle G\cong \angle J$

Hence, given congruency is proved