Question

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

Answer 1

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

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.