Question

I need to write a proof for the second property that there is one pair of congruent angles in a isosceles trapezoid (prove DA equals CB)i think it could be solved with one of the triangle congruency theorems like ASA but i dont know how

Answer 1

ABCD is a trapezium with AB=CD.

Drop perpendiculars from B and C in the below diagram.

We have BE and CF perpendicular to AD.

Now in angle ABE and CFD

BE=CF (Altitude of trapezium)

AB=CD

`\begin{gathered} \angle AEB=\angle DFC\text{ (right angle)} \\ From\text{ R.H.S congrugence} \\ \triangle ABE\cong\triangle CFD \\ \angle A=\angle D \\ Hence\text{ proved base angle of issoseles trapezium are equal.} \end{gathered}`