Answer :


Isosceles trapezium is a trapezium in which th non parallel sides are equal


Consider ABCD as the isosceles trapezium with AD = BC


We have to prove that D = C


Drop perpendiculars from point A and B on CD at points E and F respectively as shown


Consider ΔAED and ΔBFC


AD = BC … given … (i)


AE = BF … perpendiculars between two parallel lines … (ii)


Using Pythagoras theorem


DE2 = and FC2 =


Using (i) and (ii)


DE2 =


DE2 = FC2


DE = FC … (iii)


Using (i), (ii) and (iii)


Therefore, ΔAED ΔBFC


ADE = BCF … corresponding angles of congruent triangles


D = C


Hence proved


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