Question

in∆XYZ seg xy≈segxz,YQ and seg.zp are the angle Bisector of angle and y angle z respectively angle x 28° then find angle YOZ​

Answer 1

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In ∆PQR seg PM is a median. Angle bisectors of ∠PMQ and ∠PMR intersect side PQ and side PR in points X and Y respectively. Prove that XY || QR.

SOLUTION

In △PMQ, ray MX is bisector of △PMQ.

∴PXXQ=MQMP

.......... (I) theorem of angle bisector.

In △PMR, ray MY is bisector of△PMR.

∴PYYR=MRMP

.......... (II) theorem of angle bisector.

MPMQ=MPMR

......... M is the midpoint QR, hence MQ = MR.

∴PXXQ=PYYR

∴XY || QR .......... converse of basic proportionality theorem.

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