Question

given: isosceles trapezoid efgh prove: △fhe≅△geh it is given that trapezoid efgh is an isosceles trapezoid. we know that fe = gh by the definition of trapezoid. the base - angle theorem of isosceles trapezoids verifies that angle is congruent to angle. we also see that eh = eh by the property. therefore, by, we see that △fhe≅△geh.

Explanation:

Step1: Recall isosceles trapezoid property

In an isosceles trapezoid, non - parallel sides are equal. So, $\overline{FE}=\overline{GH}$ by the definition of an isosceles trapezoid.

Step2: Apply base - angle theorem

The base - angle theorem of isosceles trapezoids verifies that $\angle FEH$ is congruent to $\angle GHE$.

Step3: Consider reflexive property

We see that $\overline{EH}=\overline{EH}$ by the reflexive property.

Step4: Use congruence criterion

By the Side - Angle - Side (SAS) congruence criterion, we see that $\triangle FHE\cong\triangle GEH$.

Answer:

$\triangle FHE\cong\triangle GEH$ by SAS congruence criterion.