Question

Fill in the missing blanks below to prove that the Sum of the measures of the interior angles of a triangle is 180°.

Answer 1

Let ABC be any triangle. Draw line DE, which passes through point A, parallel to __________ with a compass and straightedge. According to the Angle Addition Postulate ∡DAB + ∡CAB + ∡CAE = ∡DAE. ∡CAE is congruent to ∡BCA by______________________. ∡DAB is congruent to ____________ by the same theorem. Substitution allows me to replace ∡CAE with ∡BCA and ∡DAB with ∡ABC in the equation. Therefore, __________________________= ∡DAE. By definition of a straight angle, ∡DAE measures ____________. Consequently, the three angles of ABC (BCA, CAB, and ABC) measure 180° by ___________.