Prove that ABC is an isosceles triangle-displaystyle frac - AP - PB - -frac - AQ - QC - and displaystyle angle APQ-angle ACB

Question

Prove that ABC is an isosceles triangle-displaystyle frac - AP - PB - -frac - AQ - QC -  and displaystyle angle APQ-angle ACB

Toppr Admin · Accepted Answer

APPB-AQQC -given-x2234-x2220-APQ-x2220-ACB - corresponding angles- -1-x2220-APQ-x2220-ACB- given-2-x2220-ABC-x2220-ACB-xA0- -from 1 -amp- 2-AB-AC-xA0- sides opposite equal angles-x2234-ABC is an isosceles triangle-

Prove that ABC is an isosceles triangle.
$\frac{A P}{P B} = \frac{A Q}{Q C}$ and $∠ A P Q = ∠ A C B$

$\frac{A P}{P B} = \frac{A Q}{Q C}$ (given)
$∴ ∠ A P Q = ∠ A C B$ ( corresponding angles) .1
$∠ A P Q = ∠ A C B$ ( given)..2
$∠ A B C = ∠ A C B$ (from 1 & 2)
$A B = A C$ ( sides opposite equal angles)
$∴ A B C$ is an isosceles triangle.

Prove that ABC is an isosceles triangle.APPB=AQQC and ∠APQ=∠ACB

APPB=AQQC (given)∴∠APQ=∠ACB ( corresponding angles) .1∠APQ=∠ACB( given)..2∠ABC=∠ACB (from 1 & 2)AB=AC ( sides opposite equal angles)∴ABC is an isosceles triangle.

Prove that ABC is an isosceles triangle.
$\frac{A P}{P B} = \frac{A Q}{Q C}$ and $∠ A P Q = ∠ A C B$

$\frac{A P}{P B} = \frac{A Q}{Q C}$ (given)
$∴ ∠ A P Q = ∠ A C B$ ( corresponding angles) .1
$∠ A P Q = ∠ A C B$ ( given)..2
$∠ A B C = ∠ A C B$ (from 1 & 2)
$A B = A C$ ( sides opposite equal angles)
$∴ A B C$ is an isosceles triangle.