Question

multiple choice 1 point
consider parallelogram lmpq and a student’s work to prove ∠q ≅ ∠m. which correctly completes the student’s proof?
step | statement | justification
1 | quadrilateral lmpq is a parallelogram. | given
2 | ql ≅ mp and qp ≅ ml |?
3 | lp ≅ lp | reflexive property
4 | δlqp ≅ δpml | side - side - side congruence theorem
5 | ∠q ≅ ∠m | corresponding parts of congruent triangles are congruent.
options:
adjacent sides of a parallelogram are congruent.
opposite sides of a parallelogram are parallel.
opposite sides of a parallelogram are congruent.
adjacent sides of a parallelogram are parallel.
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Explanation:

To prove \(\angle Q\cong\angle M\) in parallelogram \(LMPQ\), we start with the properties of a parallelogram. In a parallelogram, opposite sides are congruent. Step 1 states \(LMPQ\) is a parallelogram, so the justification for \(QL\cong MP\) and \(QP\cong ML\) (Step 2) should be the property that opposite sides of a parallelogram are congruent. Adjacent sides are not necessarily congruent or the focus here, and the "opposite sides are parallel" property is about parallelism, not congruence of sides for this step. So the correct justification is "Opposite sides of a parallelogram are congruent."

Answer:

Opposite sides of a parallelogram are congruent.