Chapter 5.1, Problem 34WE

To determine

To prove: that $\angle EGF=\angle HJI$ with the help of given information.

Answer to Problem 34WE

  $\angle EFG=\angle HJI$ by side angle side property the triangles are congruent.

Explanation of Solution

Given information:

The two parallelograms $EFIH$ and $EGJH$

System information:

  $\angle 1\cong \angle 2$

Calculation:

Consider the triangles $\text{Δ}EGF$ and $\text{Δ}HJI$

From the known statement

  $\angle 1\cong \angle 2$

In a parallelogram, opposite sides are equal

Thus,

Side $EG=sideHJ$

And

Side $EF=$ Side $HI$

Therefore, by side angle side property, the triangles are congruent.

Hence, by corresponding parts of congruent triangles $\angle EFG=\angle HJI$