Chapter 5.5, Problem 10PSA

To determine

To prove:

  $\overline{DB}$ is congruent to $\overline{CA}$ .

Explanation of Solution

Given information:

ABCDis an isosceles trapezoid.

Proof:

  

It is given that, ABCDis an isosceles trapezoid.

Bases of isosceles trapezoid are parallel.

  $\overline{AB }\parallel \overline{DC }$

Lower base angles of isosceles trapezoid are congruent.

  $\angle ABC\cong \angle BAD$

By reflexive property, we get

  $\overline{AB}\cong \overline{AB}$

Legs of isosceles trapezoid are congruent.

  $\overline{AD}\cong \overline{BC}$

Two triangles are congruent by SAS congruence rule.

  $\Delta ABC\cong \Delta BAD$

Corresponding parts of congruent triangles are congruent.

  $\overline{DB}\cong \overline{CA}$