# Thread: proving a right triangle

1. ## 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.

2. Originally Posted by sanee66
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