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 reasons 1) given 2)

Explanation:

Step1: Recall linear - pair definition

A linear pair of angles is formed when two adjacent angles form a straight - line. The sum of the measures of angles in a straight - line is 180 degrees.

Step2: State the theorem

If two angles ∠ABC and ∠CBD are a linear pair, then m∠ABC + m∠CBD=180° (by the definition of a linear pair). Supplementary angles are two angles whose sum of measures is 180°. So, ∠ABC and ∠CBD are supplementary.

Statements	Reasons
2. m∠ABC + m∠CBD = 180°	Definition of a linear pair
3. ∠ABC and ∠CBD are supplementary	Definition of supplementary angles (two angles with a sum of 180° are supplementary)

Answer:

Statements	Reasons
2. m∠ABC + m∠CBD = 180°	Definition of a linear pair
3. ∠ABC and ∠CBD are supplementary	Definition of supplementary angles