Given: ABCD is an isosceles trapezoid, GP and EQ are perpendicular to AB and DC, P and Q are midpoints of AB and DC

Prove: △AGP ≅ △DEQ

Definition
Definition
Perpendicular lines form right angles
Segment addition theorem
The base angles of an isosceles trapezoid are equal
Substitution
ASA (Angle-Side-Angle)
Algebra
Substitution
Substitution
BA = CD
AP = BP and DQ = CQ
BA = BP + AP and CD = CQ + DQ
BA = 2(PA) and CD = 2(QD)
PA = (1/2)BA and QD = (1/2)CD
PA = (1/2)BA and QD = (1/2)BA
PA = QD
∠ APG = ∠ EQD = 90
∠ A = ∠ D
△AGP ≅ △DEQ