Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

# How do you prove a triangle I isosceles by using a proof?

So I'm really stuck on this question, thank you for the help! ### 4 Answers

Relevance
• Favorite Answer

NQ || MR

∠ 1 = ∠ MRN (alternate angles equal)

∠ 2 = ∠ NMR (corresponding angles equal)

∠ 1 = ∠ 2 (since NQ bisects PNR)

Opposite angles of the triangle NMR are equal so the opposite sides are equal

NM = NR

NMR is isosceles

= means congruent to

• that one is pretty easy actually. the angle at M is the same as angle 2 (line cut by two parallel lines makes the same angles). the angle at R is equal to 1 because the opposite interior angles are equal when a line cuts two parallel lines.

1=2 by definition (formed by bisecting an angle).

• ⦤1 = ⦤NRM .............alternate angles

2*⦤1 = ⦤NRM + ⦤NMR ........... exterior angle = sum of opposite interior angles

2*⦤1 = ⦤1 + ⦤NMR

2*⦤1 - ⦤1 = ⦤NMR

⦤1 = ⦤NMR

Therefore ⦤NMR = ⦤NRM

Hence triangle NMR is an isosceles triangle

• NQ|| MR and / PM :

N2 = M

M + N + R = 180

N1 + N2 + N = 180

And N2 = M (above)

=> M + N + R = N1 + N2 + N

M + N + R = N1 + M + N

R = N1

Given: N1 = N2 => R = N2 =>

N2 = M = R

MNR is an isosceles triangle.

Still have questions? Get your answers by asking now.