Question

write the following statement in conditional form," the diagonals of isosceles trapezium are congruent" "

Answer 1

Answer:

Step-by-step explanation:

Given:

Trapezoid ABCD with AB \parallel CD.

What to show:  AC \cong BD.

Proof:

It is given that ABCD is an isosceles trapezoid with AB \parallel CD.

By the definition of isosceles trapezoid AD \cong BC.

Now, since the base angles of an isosceles trapezoid  \angle ADC \cong \angle BCD.

Also, CD \cong CD, since congruence of segments is reflexive.

By the SAS Congruence postulate, \triangle ADC \cong BCD.

AC \cong BD since corresponding parts of congruent triangles are congruent.

This completes the proof.

Therefore, diagonals of an isosceles trapezoid are congruent.