Question

write a two - column proof of the linear pairs theorem. if ∠abc and ∠cbd are a linear pair, then ∠abc and ∠cbd are supplementary. statements: 1) ∠abc and ∠cbd are a linear pair. 2) m∠abc + m∠cbd = m∠abd 3) m∠abd = 180 reasons: 1) given 2) angle addition postulate 3) definition of straight angles subtraction property of equality definition of congruent angles substitution property of equality

Explanation:

Step1: Recall linear - pair definition

If two angles form a linear pair, they are adjacent and their non - common sides form a straight line.

Step2: Apply angle addition postulate

Since ∠ABC and ∠CBD are a linear pair, by the angle addition postulate, m∠ABC + m∠CBD=m∠ABD.

Step3: Use straight - angle definition

A straight angle measures 180°. Since ∠ABD is a straight angle (formed by the non - common sides of the linear pair ∠ABC and ∠CBD), m∠ABD = 180°. So m∠ABC+m∠CBD = 180°, which means ∠ABC and ∠CBD are supplementary.

Answer:

Statements	Reasons
2) m∠ABC + m∠CBD=m∠ABD	Angle Addition Postulate
3) m∠ABD = 180	Definition of straight angles