Question

Given: Isosceles trapezoid EFGH

Prove: ΔFHE ≅ ΔGEH

Trapezoid E F G H is shown. Diagonals are drawn from point F to point H and from point G to point E. Sides F G and E H are parallel.

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 ΔFHE ≅ ΔGEH.

Answer 1

Each of the two triangles formed by the diagonals of the isosceles

trapezoid have two sides and the included angle that are congruent.

Correct response:

• ΔFHE ≅ ΔGEH by SAS rule of congruency

Methods used to prove that ΔFHE and ΔGEH are congruent

Given: Isosceles trapezoid EFGH

Required:

Prove ΔFHE ≅ ΔGEH

Solution:

The two column proof is presented as follows;

Statement  ${}$                                             Reasons

EFGH is an isosceles trapezoid ${}$         Given

FE ≅ GH ${}$                                              By definition of isosceles trapezoid

∠FEH ≅ ∠GHE ${}$                                    Base angles of an isosceles triangle

EH ≅ EH ${}$                                               By reflexive property

ΔFHE ≅ ΔGEH ${}$                   By Side–Angle–Side, SAS, rule of congruency

Given that two sides and an included angle in ΔFHE are

congruent to two sides and an included angle of ΔGEH, ΔFHE is

congruent to ΔGEH by Side-Angle-Side rule of congruency.

Learn more about the SAS rule of congruency here:

https://brainly.com/question/19654252

Answer 2

Answer:

isosceles trapezoid, FEH, GHE, Reflexive, SAS

Step-by-step explanation: