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


If AB||CD


And; AD=BC


ABCD is a isosceles trapezium


If ABCD is a isosceles trapezium


Then;


Diagonals of ABCD must be equal


AC=BD


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


∆ABD ∆ABC


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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