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If two scalene triangles are equiangular , prove that the ratio of the corresponding sides is same as the ratio of the corresponding angle bisector segment. URGENT. Please reply quickly

If two scalene triangles are equiangular , prove that the ratio of the corresponding sides is same as the ratio of the corresponding angle bisector segment.
 
URGENT. Please reply quickly 

Grade:10

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
Please find the answer to your question below
Let the two triangles be ABC and PQR
Given in triangles ABC and PQR\angleA=\angleP,\angleB=\angleQ,\angleC=\angleR
AD,PS are the bisectors of\angleA and\angleP respectively
We have to prove (AB/PQ)=(BC/QR)=(CA/RP)=(AD/PS)
\DeltaABC\sim\DeltaPQR so from given and AAA criterion
(AB/PQ)=(BC/QR)=(CA/RP)=constant........(1)
in\DeltaADC and\DeltaPSR
\angleDAC=\angleSPR.........since given (1/2)\angleA=(1/2)\angleP
\angleC=\angleR......given
So\DeltaADC\sim\DeltaPSR ….from AA criterion
So (AD/PS)=(CA/RP)........(2)
From 1 and 2(AB/PQ)=(BC/QR)=(CA/RP)=(AD/PS)
NOTE: here\Deltarepresents triangle

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