Question

write a two - column proof of the linear pairs th if ∠abc and ∠cbd are a linear pair, then ∠a 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 1) 2) 3) 4) subtraction property of equality substitution property of equality definition of congruent angles definition of complementary angles

Explanation:

Step1: Identify given equal - ities

We have two equalities: $m\angle ABC + m\angle CBD=m\angle ABD$ (Statement 2) and $m\angle ABD = 180$ (Statement 3).

Step2: Apply substitution

We substitute the value of $m\angle ABD$ from Statement 3 into Statement 2. Since $m\angle ABD$ in Statement 2 can be replaced with 180 (because they are equal according to Statement 3), we get $m\angle ABC + m\angle CBD=180$ (Statement 4).

Answer:

Substitution Property of Equality