CBSE Class 8 Answered
ABCD is a parallelogram. Side ap bisects angle A and side CQ bisects angle C. P lies on Side CD and Q lies on Side AB. show that-(1)AP||CQ
(2)AQCP is a parallelogram.
Asked by aj072263 | 28 Dec, 2018, 12:04: AM
Expert Answer
Given :- ABCD is a parallelogram. AP bisects 
A and CQ bisects C
A and CQ bisects CIn the given parallelogram, DAB = DCB. let each of angle measures α
DAB = DCB. let each of angle measures αB + DAB = B + α = 180 ...............(1)since AP and CQ are angle bisectors, we have DAP = PAQ = PCQ = BCQ = α/2
DAP = PAQ = PCQ = BCQ = α/2 AQC = B+BCQ ( exterior angle equals sum of interior angles in ΔQBChence AQC + PAQ = B+BCQ+PAQ = B + α = 180° ( using eqn.(1)
AQC + PAQ = B+BCQ+PAQ = B + α = 180° ( using eqn.(1)Sum of interior angles is 180°, hence AP || QC
also we have PC || AQ, hence AQCP is parallelogram
Answered by Thiyagarajan K | 28 Dec, 2018, 10:38: AM
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