Question

Prove the second property one pair of congruent legs is true (prove segment DA is congruent to CB)

Answer 1

he trapeziunm is an isosceles trapezoid since there are pairs of congruent base angles ADC and BCD

Lines AB and DC are the bases'

To proof that

`\bar{AD}\cong\bar{BC}`

WDraw perpendicular line segments from A to P and from B to Q which are perpendicular to line DC

∠APD =∠BQC (Right angle)

That is ∠D ≅ ∠C

Now the perpendiculars AP and BQ are congruent

By AAS Property, triangles APD and BQC are congruent and this implies that the hypotenuses AD and BC are congruent.

Therefore the legs AD and BC are congruent.