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 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. aas sss sas

Explanation:

Step1: Recall isosceles trapezoid property

In an isosceles trapezoid, non - parallel sides are congruent. So for isosceles trapezoid EFGH, FE ≅ GH.

Step2: Apply base - angle theorem

The base - angle theorem of isosceles trapezoids states that base angles are congruent. So ∠FEH is congruent to ∠GHE.

Step3: Identify reflexive property

EH ≅ EH by the reflexive property (a segment is congruent to itself).

Step4: Determine congruence criterion

We have two sides and the included angle congruent (FE ≅ GH, ∠FEH ≅ ∠GHE, EH ≅ EH), so by the SAS (Side - Angle - Side) congruence criterion, △FHE ≅ △GEH.

Answer:

1. Non - parallel sides of an isosceles trapezoid
2. ∠FEH
3. ∠GHE
4. Reflexive
5. SAS