Question

Given: AD ICB, use a two-column proof to prove that mZ1+mZ2 + m _3 = 180°. You may not use Triangle Interior Angle Sum Theorem as a reason in your proof.

a) Provides a valid two-column proof
b) Provides an incorrect proof
c) Provides an incomplete proof
d) Does not address the question

Answer 1

For a two-column proof that m∠1 + m∠2 + m∠_3 = 180°, one must use the properties of parallel lines and angles formed by a transversal to show that the sum of these angles is equal to the straight line angle sum.

Step-by-step explanation:

The question asks for a two-column proof to demonstrate that the sum of the measures of three angles (m∠1 + m∠2 + m∠_3) equals 180° without using the Triangle Interior Angle Sum Theorem. This is a classical geometry problem that requires an understanding of parallel lines and the properties of transversals and angles. As per the instructions, the proof must be derived by logically deducing from the given that line AD is parallel to line CB (AD ∥CB).

To start the proof, you would state that since AD is parallel to CB and a transversal (AB) cuts them, corresponding angles are congruent. Next, you would show that the sum of angles on a straight line (such as angle 1 and angle 3 with angle ABB') equals 180°. With these pieces of information, you can deduce that angle 2 is supplementary to angle ABB', which is congruent to angle 1. Hence, angle 1, angle 2, and angle 3 add up to 180°.