Prove the following theorem is true: “The diagonals of an isosceles trapezoid are congruent.”?

Question

Prove the following theorem is true: “The diagonals of an isosceles trapezoid are congruent.”

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Given:
Trapezoid EFGH with bases FG and EH
FE is congruent to GH

Prove:
EG is congruent to HF

I took a shot at this question and seemed to be wrong. My teacher left me this feedback and the answer I came up with had slim to no sense of the question. Mind helping?

INSTRUCTOR COMMENTS:

Hint. Use the distance formula to find the length of the diagonals FH and EG. ( See lesson 1.05 for help with the distance formula.) Then compare the lengths of EG and FH.

Answer 1

No sweat, partner.

EH=EH Identity
mAngle E = mAngleH Property of isos. trap.
EF=GH Given
EFH congruent to HGE SAS=SAS
EG=FH Corresponding sides

Answer 2

FH = GE because all diagonals in a trapezoid are congruent.

Answer 3

distance formula:

d^2 = (x2 - x1)^2 + (y2 - y1)^2

d^2 = ( a - (-b)^2 + (0 - c)^2

d^2 = (a + b)^2 + (-c)^2

d^2 = a + 2ab + b^2 + c^2

d = sqrt (a + 2ab + b^2 + c^2)

samething with the other digonal
d^2 = (b - (-a) )^2 + (c - 0)^2

d^2 = (b + a)^2 + (c)^2

d^2 = (b^2 + 2ab + a^2 + c^2)

d^2 = sqrt(b^2 + 2ab + a^2 + c^2)


sqrt(b^2 + 2ab + a^2 + c^2) = sqrt (a + 2ab + b^2 + c^2)

so the two digonals are congruent