Question

ABCD IS A CYCLIC QUADRILATERAL WITH AD||BC. PROVE THAT AB=DC

Answer 1

student-name Amirtha Varshini asked in Math
ABCD is a cyclic quadrilateral with AD PARALLEL BC Prove AB=CD
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student-name Lalit Mehra answered this
in Math, Class
Hi!
Here is the answer to your question.
Given: ABCD is a cyclic quadrilateral and AD || BC.
To prove: AB = CD
Construction: Draw AE ⊥ BC and DF ⊥ BC.

Proof: AD || BC

∴ ∠ADC + ∠DCF = 180° (sum of adjacent interior angles is 180°)
∠ABE + ∠ADC = 180° (sum of opposite angles of cyclic quadrilateral is 180°)
⇒ ∠ADC + ∠DCF = ∠ABE + ∠ADC
⇒ ∠DCF = ∠ABE

In DABE and DDCF, we have
∠ABE = ∠DCF (proved)
∠AEB = ∠DFC (90°)
AE = DF (distance between the parallel sides is same)
∴ DABE ≅ DDCF (AAS congruence criterion)
⇒ AB = CD (C.P.C.T)



Hope it helps
Thanks
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Answer 2

Answer:

Refer the attachment, Hope it helps and if it does please mark as brainliest