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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!

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4 Answers

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  • cidyah
    Lv 7
    3 years ago
    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

  • 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.

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