4. In the adjoining figure, line segments AB and CD bisect eachother a

1.	4. In the adjoining figure, line segments AB and CD bisect eachother at O.Prove that:(i) AC DB and(ii) AD-CB.
Answer» Since,ACandBDbisecteachotheratO, thenOA=OBandOC=OD In∆AOCand∆BOD,OA=OB Given∠AOC=∠BOD VerticallyoppositeanglesOC=OD Given⇒∆AOC≅∆BODSAS ⇒AC=BDCPCT ∠CAO=∠OBDCPCT ⇒∠CAB=∠ABD In∆AODand∆BOC,OA=OB Given∠AOD=∠BOC VerticallyoppositeanglesOD=OC Given⇒∆AOD≅∆BOCSAS ⇒AD=CBCPCT ⇒∠OAD=∠OBCCPCT But∠OADand∠OBCarealternateinterioranglesmadebythetransversalABwithlinesADandBCandareequal. So,AD∥CB Thanks Can i have your fb account please

4. In the adjoining figure, line segments AB and CD bisect eachother at O.Prove that:(i) AC DB and(ii) AD-CB.

Answer»

Since,ACandBDbisecteachotheratO,

thenOA=OBandOC=OD

In∆AOCand∆BOD,OA=OB

Given∠AOC=∠BOD

VerticallyoppositeanglesOC=OD

Given⇒∆AOC≅∆BODSAS

⇒AC=BDCPCT

∠CAO=∠OBDCPCT

⇒∠CAB=∠ABD

In∆AODand∆BOC,OA=OB

Given∠AOD=∠BOC

VerticallyoppositeanglesOD=OC

Given⇒∆AOD≅∆BOCSAS

⇒AD=CBCPCT

⇒∠OAD=∠OBCCPCT

But∠OADand∠OBCarealternateinterioranglesmadebythetransversalABwithlinesADandBCandareequal.

So,AD∥CB

Thanks

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