If a pair of opposite sides of a cylic quadrilateral are equal, prove that its diagonals are equal. [3 MARKS]
Concept: 1 Mark
Steps: 1 Mark
Answer: 1 Mark
Given: A cyclic quadrilateral ABCD in which AB = DC.
To Prove: Diagonal AC = Diagonal BD.
Proof :
∠BAC=∠BDC ..... (i) [Angles in the same segment of a circle. ]
∠CAD=∠ADB .....(ii) [ Equal arcs CD and AB subtend equal angles at the circumference ]
∠BAC+∠CAD=∠BDC+∠ADB [Adding (i) and (ii)]
⇒∠BAD=∠ADC
⇒BD=AC [Equal angles on the same circle cut off equal chords.]
⇒ diagonal AC=diagonal BD.
Hence Proved.