Question

prove that diagonal of a isosceles trapezium are congruent

Answer 1

We have to know the features of an isosceles trapezium first.

In an isosceles trapezium,

  ⇒  One pair of opposite sides are equal but not parallel.

  ⇒  One pair of opposite sides are parallel but not equal.

  ⇒  Angles on either end of one among the parallel sides are equal.

  ⇒  Angles on either end of one among the equal sides are supplementary.

The proof is given below:

Consider the isosceles trapezium ABCD given in the figure.

We have to prove that AC = BD.

Consider triangles ABC and BAD.

    →  AB = AB (common)

    →  BC = AD

    →  ∠B = ∠A

∴ ΔABC ≅ ΔBAD

∴ AC = BD

Hence Proved!!!