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

Click or touch to draw on the diagram
Perpendicular lines form right angles
Algebra
Segment addition theorem
Substitution
Substitution
Definition
ASA (Angle-Side-Angle)
The base angles of an isosceles trapezoid are equal
Substitution
Definition
BA = CD
AP = BP and DQ = CQ
BA = BP + AP and CD = CQ + DQ
BA = 2(PA) and CD = 2(QD)
$$PA = \frac{1}{2}BA$$ and $$QD = \frac{1}{2}CD$$
$$PA = \frac{1}{2}BA$$ and $$QD = \frac{1}{2}BA$$
PA = QD
$$\angle APG = \angle EQD = 90^\circ$$
∠ A = ∠ D
△AGP ≅ △DEQ