Question

problem e
given: parallelogram defg, \\( \overline { d h } \cong \overline { f i } \\)
prove: \\( \angle d e h \cong \angle f g i \\)

1. parallelogram defg 1. given
2. click here to insert 2. if a quadrilateral is a parallelogram, then both pairs of opposite sides are congruent.
3. click here to insert 3. definition of a parallelogram
4. click here to insert 4.

Explanation:

Step1: Use the property of parallelogram

$$\overline{DE}\cong\overline{FG}$$

Step2: Use the property of parallelogram

$$\overline{DE}\parallel\overline{FG}$$

Step3: Use the property of parallel lines

$$\angle EDH\cong\angle GFI$$

Step4: Prove triangles congruent

By SAS (Side - Angle - Side) congruence criterion, $\triangle DEH\cong\triangle FGI$. Then $\angle DEH\cong\angle FGI$ (Corresponding parts of congruent triangles are congruent)

Answer:

$\angle DEH\cong\angle FGI$