Question

PLEASE HELP!!!!

Determine if the conclusion is valid. Give a thorough explanation of your answer.
D
B
Given: AB || DC, AD || BC, AB BC
Conclusion: ABCD is a rhombus.

Answer 1

Answer: Correct

Explanation:

The conclusion is valid. Since
`\overline{AB} \parallel \overline{DC}` and
`\overline{AD} \parallel \overline{BC}`, we know that ABCD is a parallelogram because it has two pairs of parallel sides. Also, since
`\overline{AB} \cong \overline{BC}`, we know that ABCD is a parallelogram with a pair of consecutive congruent sides, making it a rhombus.