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If the two sides of a pair of opposite s...

If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, then

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Given Let ABCD be a cyclic quadrilateral and AD=BC.

Join AC and BD.
To prove AC=BD
Proof In `DeltaAOD and DeltaBOC`,
`angleOAD=angleOBC`
` "and "angleODA=angleOCB`
[since, same segments subtends equal angle to the circle]
AB=BC [given]
`:. DeltaAOD cong DeltaBOC ` [by ASA congruence rule]
Adding `DeltaDOC` on both sides, we get
`DeltaAOD+DeltaDOC cong DeltaBOC+ DeltaDOC`
`rArr Delta ADC cong Delta BCD`
`:. AC = BD ` [by CPCT]
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