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