Answer to Question #148310 in Geometry for J

Question

Prove that the base angles of an isoceles trapezoid are congruent.

Answer 1

Given: ABCD is a trapezoid, AB||DC, and AD is congruent to BC

Prove: Angle A is congruent to Angle ABC

1. Before you begin, draw a line parallel to AD from B and name it BX, AD||BX.

2. ABXD is a parallelogram (opposite sides of a parallelogram are parallel)

3. AD is congruent to BX (opposite sides of a parallelogram are congruent)

4. BC is congruent to BX (transitive property)

5. Angle BXC is congruent to Angle C (angles opposite congruent sides are congruent)

6. Angle D is congruent to Angle BXC (If two parallel lines are cut by a transversal DC, corresponding angles are congruent)

7. Angle D is congruent to Angle C (Transitive property)

8. Angle D is supplementary to Angle A

Angle C is supplementary to Angle ABC

(If two parallel lines are cut by a transversal, interior angles on the same side of a transversal are supplementary)

9. Angle A is congruent to Angle ABC (supplements of congruent angles are congruent)