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
4. m∠abc + m∠cbd = 180

reasons

1. given
2. angle addition postulate
3. definition of straight angles
4. subtraction property of equality

definition of congruent angles
substitution property of equality
definition of complementary angles

Explanation:

Step1: State given information

1. $\angle ABC$ and $\angle CBD$ are a linear - pair. (Given)

Step2: Apply Angle Addition Postulate

1. $m\angle ABC + m\angle CBD=m\angle ABD$ (Angle Addition Postulate)

Step3: Recall the measure of a straight - angle

1. $m\angle ABD = 180$ (Definition of straight angles)

Step4: Substitute the value of $m\angle ABD$

1. Since $m\angle ABC + m\angle CBD=m\angle ABD$ and $m\angle ABD = 180$, by the Substitution Property of Equality, $m\angle ABC + m\angle CBD = 180$.

Answer:

1. Substitution Property of Equality