Prove that the base angles of an isosceles trapezium are equal.

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Solution

Let ABCD be an isosceles trapezium, where AD = BC and AB || CD.

Draw perpendiculars AM and BN

Consider ΔADM and ΔBNC.

AD = BC

AM = BN (Perpendicular distance between two parallels is same)

Therefore, from SAS congruency, we get:

Hence, the base angles of an isosceles trapezium are equal.

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