Question

I'm stuck and really need help. I can't figure out the rest.

Answer 1

Answer:

The next statements are are;

Statement                                                  ${}$        Reason

Segment $\overline {DC}$ ≅ Segment $\overline {AB}$                        ${}$   CPCTC

$\overline {AD}$ ≅ $\overline {BC}$ and $\overline {DC}$ ≅ $\overline {AB}$, therefore;

ABCD is a parallelogram                    ${}$               Parallelogram side theorem

Step-by-step explanation:

Statement                                                  ${}$        Reason

Segment $\overline {DC}$ ≅ Segment $\overline {AB}$  by Congruent Parts of Congruent Triangles are Congruent (CPCTC)

Given that $\overline {AD}$ ≅ $\overline {BC}$ and we have that $\overline {DC}$ ≅ $\overline {AB}$, we get;

ABCD is a parallelogram                    ${}$               Parallelogram side theorem

The parallelogram side theorem states that a quadrilateral is a parallelogram if it has two pairs or sets of congruent opposite sides.