Question

Match each statement in the proof with the correct reason.

Answer 1

Answer:

See explanation

Step-by-step explanation:

Definition of parallelogram: Parallelogram is a quadrilateral with two pairs of parallel sides.    

Definition of transversal (diagonal): A line that cuts across two or more (usually parallel) lines.

Definition of the same side interior angles: These angles are located exactly as their name describes. They are "interior" (between the parallel lines), and they are on the same side of the transversal (diagonal).

The same-side interior angles theorem states that when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary

       Statement                          Reason

1. ABCD is a parallelogram  -  Given

2. $\overline{AB}\parallel \overline {CD}$                           -  Definition of parallelogram

3. $\overline{AD}$ is a diagonal of $\overline{AB}$ and $\overline{CD}$ - Definition of diagonal

4.  $\angle A$ and $\angle D$ are the same side interior angles - Definition of same-side interior angles

5.  $\angle A$ is supplementary to  $\angle D$ - Same-Side Interior Angles Theorem