Proof of the angle sum theoremAngle sum theorem: The angle measures in any triangles add up to 180 degrees Key concept: Alternate interior angles are equal. We will accept this fact without a proof For the pair in red, angle 1 = angle 2. For the pair in blue, angle 3 = angle 4 Now, take a close look at the figure below. I claim that angle x is equal to 85 degrees so the sum is 180 degrees Angle b = 30 degrees because it alternates with the angle inside the triangle that measures 30 degrees Looking at the figure again, it is easy to see why angle x is 85. Since the 65 degrees angle, the angle x, and the 30 degrees angle make a straight line together, the sum must be 180 degrees Since, 65 + angle x + 30 = 180, angle x must be 85 This is not a proof yet. This just shows that it works for one specific example Proof of the angle sum theorem: Start with the following triangle with arbitrary values for the angles: angle a + angle b + angle c = 180 degrees Since alternate interior angles are equal, angle a = angle x and angle b = angle y Therefore, angle x + angle y + angle c = 180 degrees 




Are you a fan of this site? Support us Our awards! Our partners About me Disclaimer Build your website! Advertise on my site Try our free toolbar Like us on Facebook Take our survey Illustrated fractions Educational math software Math jobs Best Teacher Sites Now Teachers/Students tools Search math jobs Algebra ebook Fraction ebook Geometric formulas ebook 