Chapter 6.3, Problem 56SPR

To determine

To prove: $\Delta EJG\cong \Delta FKH$

Explanation of Solution

Given information: $\overline{EJ}\parallel \overline{FK},\overline{JG}\parallel \overline{KH}$ and $\overline{EF}\cong \overline{GH}$

Proof: Let $P$ be the point where $\overline{FK}$ and $\overline{JG}$ intersects.

Since $\overline{JG}\parallel \overline{KH}$ , $\overline{JG}\parallel \overline{PG}$ and by definition of being similar, all angles are congruent.

  $\therefore \Delta PFG\sim \Delta FKH$

Similarly $\overline{FK}\parallel \overline{EJ}$ , $\overline{FK}\parallel \overline{FP}$ and by definition of being similar, all angles are congruent.

  $\therefore \Delta FPG\sim \Delta EJG$

As $\overline{EG}\cong \overline{FH}$ , they share common sides. So, both triangles are similar to each other.

  $\therefore \Delta EJG\cong \Delta FKH$