# 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!

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• cidyah
Lv 7
3 years ago

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

• 3 years ago

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).

• 3 years ago

⦤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

• mizoo
Lv 7
3 years ago

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.