Grade 1010 grade maths

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

Siddharth Gurla

11 Years agoGrade 10

1 Answer

SHAIK AASIF AHAMED

Approved Tutor Answer11 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 $\angle$ A= $\angle$ P, $\angle$ B= $\angle$ Q, $\angle$ C= $\angle$ R
AD,PS are the bisectors of $\angle$ A and $\angle$ P respectively
We have to prove (AB/PQ)=(BC/QR)=(CA/RP)=(AD/PS)
$\Delta$ ABC $\sim$ $\Delta$ PQR so from given and AAA criterion
(AB/PQ)=(BC/QR)=(CA/RP)=constant........(1)
in $\Delta$ ADC and $\Delta$ PSR
$\angle$ DAC= $\angle$ SPR.........since given (1/2) $\angle$ A=(1/2) $\angle$ P
$\angle$ C= $\angle$ R......given
So $\Delta$ ADC $\sim$ $\Delta$ PSR ….from AA criterion
So (AD/PS)=(CA/RP)........(2)
From 1 and 2(AB/PQ)=(BC/QR)=(CA/RP)=(AD/PS)
NOTE: here $\Delta$ represents triangle