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 reasons

1. ∠abc and ∠cbd are a linear pair. 1) given
2. m∠abc + m∠cbd = m∠abd 2) angle addition postulate
3. m∠abd = 180 3) definition of straight angles
4. m∠abc + m∠cbd = 180 4)

Explanation:

Step1: Recall previous statements

We have $m\angle ABC + m\angle CBD=m\angle ABD$ (from Angle - Addition Postulate) and $m\angle ABD = 180$ (from definition of straight - angles).

Step2: Substitute

Substitute $m\angle ABD$ in the first equation. Since $m\angle ABD = 180$, we get $m\angle ABC + m\angle CBD=180$.

Answer:

Substitution Property of Equality