Question

Prove that: Base angles of an isosceles trapezium are congruent.

Answer 1

Let $\square$ABCD be an isosceles trapezium in which AD = BC.

To prove: $\angle$D = $\angle$C, i.e., base angles are equal.
Construction:
We draw AP $\perp$ CD and BQ $\perp$ CD.
Proof:
In ΔAPD and ΔBQC we have:
$\angle$APD = $\angle$BQC [ 90°each]
AD = BC [Given]
AP = BQ [Height of the trapezium]
By the RHS congruency criteria, we have:
ΔAPD $\cong$ ΔBQC
$\Rightarrow$$\angle$ADP = $\angle$BCQ [by c.a.c.t]