Question

Find something interesting to prove. Then prove it. Answers may vary.

Given: $▱\mathrm{EFIH};▱\mathrm{EGHJ};\angle 1\cong \angle 2$

Short answer

It is proved that $\angle EGF\cong \angle HJI$.

Step-by-step solution

Step 1. Description of step.

The opposite sides of a parallelogram are congruent.

In $▱EFIH$, $\overline{EF}$and $\overline{HI}$are the opposite sides of a parallelogram therefore, $\overline{EF}\cong \overline{HI}$.

In $▱EGHJ$, $\overline{EG}$and $\overline{HJ}$are the opposite sides of a parallelogram therefore,$\overline{EG}\cong \overline{HJ}$.

Step 2. Description of step.

Consider $\Delta EGF$and $\Delta HJI$in which $\overline{EF}\cong \overline{HI}$,$\overline{EG}\cong \overline{HJ}$ and$\angle 1\cong \angle 2$ then by SAS postulate $\Delta EGF\cong \Delta HJI$.

Step 3. Description of step.

As $\Delta EGF\cong \Delta HJI$, then by corresponding parts of congruent triangles, $\angle EGF\cong \angle HJI$.

Therefore, it is proved that $\angle EGF\cong \angle HJI$.