Question

plzz answer the all questions
and plzz it's my request only who answer those who are confidence for the answer.
(plzz right answer is will be brainliest answer.)
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Answer 1

$\mathtt \orange{answer}$

$\boxed {\blue {GIVEN:- }}$

$\small{\triangle PQR \: is \: an \: isoceles \: triangle \: in \: which PQ=PR }$

$LM \parallel QR$

$\boxed {\red {solution:- }}$

$\huge{ i)}$

we have to prove,

$\angle Q= \angle R$

REASON:-

it is equal bcz we know that the opposite angle of equal sides are equal that's why

$\angle Q= \angle R$

$\huge{ ii)}$

in this we have to prove,

$\angle PLM= \angle Q$

REASON:-

these angles are equal bcz they are corresponding angles of parallel lines which are equals that's why

$\angle PLM= \angle Q$

$\huge{ iii)}$

in this we have to prove,

$\angle PML= \angle \R$

REASON:-

THESE ANGLES ARE ALSO CORRESPONDING ANGLES OF THE PARALLEL LINES THAT'S WHY

$\angle PML= \angle R$

$\huge{ iv)}$

we have to prove,

$\angle PLM= \angle PML$

SOLUTION:-

we have proved in 1st part that

$\angle Q= \angle R....eq(i)$

we proved in 2nd part that

$\angle PLM= \angle Q.....eq(ii)$

we have proved in 3rd part that

$\angle PML= \angle R.....eq(iii)$

by observing all 3 eq. we conclude that

$\angle PLM= \angle PML$

hence, proved

$\huge{ v)}$

we have to prove that

$\triangle PLM \: is \: an \: isoceles \: triangle$

SOLUTION:-

we have proved in 2nd part that

$\angle PLM= \angle Q .....eq.(i)$

we have proved in 3rd part that

$\angle PML= \angle R......(ii)$

by observing both eq. we conclude that

$\angle PLM= \angle PML$

we know that opp. angles of any triangle is equal so it is a isosceles triangle.

hence proved.

$\triangle PLM \: is \: an \: isoceles \: triangle$