Chapter 3.2, Problem 4PSA

To determine

To prove : The congruency of $\Delta EFJ\cong \Delta HFG$ is to be proved

Explanation of Solution

Given information : The following information has been given

  $\angle 1\cong \angle 2$

  $\overrightarrow{EF}\cong \overrightarrow{HF}$

Formula used : Two triangles are congruent by angle-side-angle property, if there are two congruent angles, and the side between them is also congruent

Proof : As we can see in the diagram, $\angle 3$ and $\angle 4$ are vertically opposite angles, hence we can say that

  $\angle 3\cong \angle 4$

And, we also know that

  $\angle 1\cong \angle 2$

  $\overrightarrow{EF}\cong \overrightarrow{HF}$

Thus, as mentioned in the formula above, by ASA property we can say that the triangle

  $\Delta EFJ\cong \Delta HFG$

Hence, given congruency is proved