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Math Help - proving a right triangle

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    proving a right triangle

    how do i go about proving ABC is a right triangle?
    ACF and CDE are equilateral triangles and b + d = 90 degrees. Prove that ABC is a right triangle.
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    Quote Originally Posted by sanee66 View Post
    how do i go about proving ABC is a right triangle?
    ACF and CDE are equilateral triangles and b + d = 90 degrees. Prove that ABC is a right triangle.
    angles e, f and a are supplimentary (they add up to 180). since triangles ACF and CDE are equilateral, all their angles are 60. so a = f = 60. which means that e = 180 - 2(60) = 60

    again, since triangle ACF is equilateral, angle b = 60. so since b + d = 90, we have d = 90 - 60 = 30.

    now the angles of a triangle add up to 180. so for triangle ABC, d + e + g = 180.

    => 30 + 60 + g = 180
    => g = 180 - 30 - 60 = 90

    since one of the angles of triangle ABC is 90, it is a right-triangle
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