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ABC is a triangle where three …

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ABC is a triangle where three lines are drawn through the vertices A, B and C parallel to the sides BC, CA and AB respectively, forming triangle PQR. Prove that BC=1/2PR, AC=1/2PQ, AB=1/2RQ

Posted by Aastha Shetty 4 years, 9 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 4 years, 9 months ago

Given: {tex}\triangle{/tex}ABC, lines are drawn through A, B and C parallel respectively to the sides BC, CA and AB forming {tex}\triangle{/tex}PQR.

To Prove : BC = {tex}\frac{1}{2}{/tex}QR
Proof : AQ || CB and AC || QB
{tex}\therefore{/tex} AQBC is a parallelogram
{tex}\therefore{/tex} BC = QA . . . [Opp. sides of a || gm] . . .(1)
As AR || BC and AB || RC
{tex}\therefore{/tex} ARCB is a parallelogram.
{tex}\therefore{/tex} BC = AR . . .[Opp. sides of a || gm] . . . (2)
QA = AR = {tex}\frac{1}{2}{/tex}QR . . . [From (1) and (2)] . . . (3)
BC = {tex}\frac{1}{2}{/tex}QR . . . .[From (1) and (3)]

ANSWER

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