Question

6 multiple choice 1 point consider parallelogram lmpq and a students work to prove ∠q ≅ ∠m. which correctly completes the students proof? step statement justification 1 quadrilateral lmpq is a parallelogram. given 2 \\( \overline { q l } \cong \overline { m p } \\) and \\( \overline { q p } \cong \overline { m l } \\) ? 3 \\( \overline { l p } \cong \overline { l p } \\) reflexive property 4 \\( \triangle l q p \cong \triangle p m l \\) side-side-side congruence theorem 5 \\( \angle q \cong \angle m \\) corresponding parts of congruent triangles are congruent. adjacent sides of a parallelogram are parallel. adjacent sides of a parallelogram are congruent. opposite sides of a parallelogram are congruent. opposite sides of a parallelogram are parallel. clear my selection

Explanation:

To determine the correct justification for step 2, we recall the properties of a parallelogram. In a parallelogram, opposite sides are congruent. The statement in step 2 is about the congruence of sides \(\overline{QL}\) and \(\overline{MP}\), and \(\overline{QP}\) and \(\overline{ML}\), which are opposite sides of parallelogram \(LMPQ\).

• The first option is incorrect because adjacent sides of a parallelogram are not necessarily congruent (unless it's a rhombus) and the statement is about parallelism, not congruence.
• The second option is incorrect as adjacent sides of a parallelogram are not congruent in general.
• The third option is correct because it states the property that opposite sides of a parallelogram are congruent, which matches the congruence of the opposite sides in the statement.
• The fourth option is incorrect as it is about the parallelism of opposite sides, not their congruence.

Answer:

C. Opposite sides of a parallelogram are congruent.