Q. 34.3( 40 Votes )

ABCD is trapezium

Answer :

Given:- ABCD is a isosceles trapezium

Trapezium with one pair of sides is parallel

And other pair of sides is equal[AD=BC].

Formula used:- SSS congruency property

If all 3 sides of triangle are equal to all 3 sides of

other triangle

Then; Both triangles are congruent

Solution:- In trapezium ABCD


And; AD=BC

ABCD is a isosceles trapezium

If ABCD is a isosceles trapezium


Diagonals of ABCD must be equal


In Δ ABD and Δ ABC

AC=BD [ ABCD is isosceles trapezium]

AD=BC [Given]

AB=AB [Common line in both triangle]

Both triangles are congruent by SSS property


If both triangles are congruent

Then there were also be equal.

A= B

As ABCD is trapezium and AB||CD

A+ D=180° and C+ B=180°

A =180° - D and B=180° - C

If A= B;

180° - D=180° - C

180° + C - 180° = D

C= D;

Conclusion:- If ABCD is trapezium in which AD = BC, then A = B and C = D.

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