Q5 of 33 Page 108

Let us prove that in an isosceles trapezium the two angles adjacent to any parallel sides are equal.


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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