In parellogram ABCD, two points P and Q are taken on diagonal BD such that DP= BQ 1. TriangleAPD= triangle CQB .2. AP= CQ .3.triangle AQB= triangle CPD AQ=CP APCQ is a parellogram
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In parallelogram ABCD, two points PP and QQ are taken on diagonal BD such that DP=BQDP=BQ seefigureseefigure. Show that:
In parallelogram ABCD, two points PP and QQ are taken on diagonal BD such that DP=BQDP=BQ seefigureseefigure. Show that:ii ΔAPD≅ΔCQBΔAPD≅ΔCQB
In parallelogram ABCD, two points PP and QQ are taken on diagonal BD such that DP=BQDP=BQ seefigureseefigure. Show that:ii ΔAPD≅ΔCQBΔAPD≅ΔCQBiiii AP=CQAP=Ciiiiii ΔAQB≅ΔCPDΔAQB≅ΔCPD
In parallelogram ABCD, two points PP and QQ are taken on diagonal BD such that DP=BQDP=BQ seefigureseefigure. Show that:ii ΔAPD≅ΔCQBΔAPD≅ΔCQBiiii AP=CQAP=Ciiiiii ΔAQB≅ΔCPDΔAQB≅ΔCPDiviv AQ=CPAQ=CP
In parallelogram ABCD, two points PP and QQ are taken on diagonal BD such that DP=BQDP=BQ seefigureseefigure. Show that:ii ΔAPD≅ΔCQBΔAPD≅ΔCQBiiii AP=CQAP=Ciiiiii ΔAQB≅ΔCPDΔAQB≅ΔCPDiviv AQ=CPAQ=CPvv APCQ is a parallelogram.
Consider triangles APD and CQB, AD ∥BC‖BC and BDBD is transversal.
Consider triangles APD and CQB, AD ∥BC‖BC and BDBD is transversal.∴∠1=∠2∴∠1=∠2
Consider triangles APD and CQB, AD ∥BC‖BC and BDBD is transversal.∴∠1=∠2∴∠1=∠2AD =BC[=BC[ Opposite sides of a parallelogram]
Consider triangles APD and CQB, AD ∥BC‖BC and BDBD is transversal.∴∠1=∠2∴∠1=∠2AD =BC[=BC[ Opposite sides of a parallelogram]DP=BQDP=BQ
Consider triangles APD and CQB, AD ∥BC‖BC and BDBD is transversal.∴∠1=∠2∴∠1=∠2AD =BC[=BC[ Opposite sides of a parallelogram]DP=BQDP=BQGivenGiven
Consider triangles APD and CQB, AD ∥BC‖BC and BDBD is transversal.∴∠1=∠2∴∠1=∠2AD =BC[=BC[ Opposite sides of a parallelogram]DP=BQDP=BQGivenGiven∴ΔAPD≡ΔCQB∴ΔAPD≡ΔCQB
Consider triangles APD and CQB, AD ∥BC‖BC and BDBD is transversal.∴∠1=∠2∴∠1=∠2AD =BC[=BC[ Opposite sides of a parallelogram]DP=BQDP=BQGivenGiven∴ΔAPD≡ΔCQB∴ΔAPD≡ΔCQB(ii)(ii) AP=CQAP=CQ
Consider triangles APD and CQB, AD ∥BC‖BC and BDBD is transversal.∴∠1=∠2∴∠1=∠2AD =BC[=BC[ Opposite sides of a parallelogram]DP=BQDP=BQGivenGiven∴ΔAPD≡ΔCQB∴ΔAPD≡ΔCQB(ii)(ii) AP=CQAP=CQCPCTCPCT
Consider triangles APD and CQB, AD ∥BC‖BC and BDBD is transversal.∴∠1=∠2∴∠1=∠2AD =BC[=BC[ Opposite sides of a parallelogram]DP=BQDP=BQGivenGiven∴ΔAPD≡ΔCQB∴ΔAPD≡ΔCQB(ii)(ii) AP=CQAP=CQCPCTCPCTFromresult(\(i\))Fromresult(\(i\))
Consider triangles APD and CQB, AD ∥BC‖BC and BDBD is transversal.∴∠1=∠2∴∠1=∠2AD =BC[=BC[ Opposite sides of a parallelogram]DP=BQDP=BQGivenGiven∴ΔAPD≡ΔCQB∴ΔAPD≡ΔCQB(ii)(ii) AP=CQAP=CQCPCTCPCTFromresult(\(i\))Fromresult(\(i\))iiiiii Consider triangles AQB and CPD,
Consider triangles APD and CQB, AD ∥BC‖BC and BDBD is transversal.∴∠1=∠2∴∠1=∠2AD =BC[=BC[ Opposite sides of a parallelogram]DP=BQDP=BQGivenGiven∴ΔAPD≡ΔCQB∴ΔAPD≡ΔCQB(ii)(ii) AP=CQAP=CQCPCTCPCTFromresult(\(i\))Fromresult(\(i\))iiiiii Consider triangles AQB and CPD,AB=CDAB=CD
Consider triangles APD and CQB, AD ∥BC‖BC and BDBD is transversal.∴∠1=∠2∴∠1=∠2AD =BC[=BC[ Opposite sides of a parallelogram]DP=BQDP=BQGivenGiven∴ΔAPD≡ΔCQB∴ΔAPD≡ΔCQB(ii)(ii) AP=CQAP=CQCPCTCPCTFromresult(\(i\))Fromresult(\(i\))iiiiii Consider triangles AQB and CPD,AB=CDAB=CDOppositesidesofaparallelogramOppositesidesofaparallelogram
Consider triangles APD and CQB, AD ∥BC‖BC and BDBD is transversal.∴∠1=∠2∴∠1=∠2AD =BC[=BC[ Opposite sides of a parallelogram]DP=BQDP=BQGivenGiven∴ΔAPD≡ΔCQB∴ΔAPD≡ΔCQB(ii)(ii) AP=CQAP=CQCPCTCPCTFromresult(\(i\))Fromresult(\(i\))iiiiii Consider triangles AQB and CPD,AB=CDAB=CDOppositesidesofaparallelogramOppositesidesofaparallelogram∠ABQ=∠CDP[∠ABQ=∠CDP[ Alternate interior angles as AB ∥‖ CD and BD is transversal]
Consider triangles APD and CQB, AD ∥BC‖BC and BDBD is transversal.∴∠1=∠2∴∠1=∠2AD =BC[=BC[ Opposite sides of a parallelogram]DP=BQDP=BQGivenGiven∴ΔAPD≡ΔCQB∴ΔAPD≡ΔCQB(ii)(ii) AP=CQAP=CQCPCTCPCTFromresult(\(i\))Fromresult(\(i\))iiiiii Consider triangles AQB and CPD,AB=CDAB=CDOppositesidesofaparallelogramOppositesidesofaparallelogram∠ABQ=∠CDP[∠ABQ=∠CDP[ Alternate interior angles as AB ∥‖ CD and BD is transversal]BQ∴=DP [Given]ΔAQB≅ΔCPDBQ=DP [Given]∴ΔAQB≅ΔCPD