Question

problem 16: (first taught in lesson 27) from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: ∠a and ∠adc are supplementary. prove: ab || dc

Explanation:

Step1: Identify the angles

$\angle A$ and $\angle ADC$ are interior angles on the same side of the transversal $\overline{AD}$.

Step2: Apply the theorem

Since $\angle A$ and $\angle ADC$ are supplementary, by the theorem "If two - interior angles on the same side of a transversal are supplementary, then the two lines are parallel", we can conclude that $\overline{AB}\parallel\overline{DC}$.

Answer:

If two - interior angles on the same side of a transversal are supplementary, then the two lines are parallel.