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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!
- cidyahLv 73 years agoFavorite 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
- busterwasmycatLv 73 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).
- BrainardLv 73 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
- mizooLv 73 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.