QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
# Proving the Converse of the Parallelogram Side Theorem
Given: LM ≅ ON and LO ≅ MN Prove: LMNO is a parallelogram.
Assemble the proof by dragging tiles to the Statements and Reasons columns.
| Angles | Segments | Triangles | Statements | Reasons |
| --- | --- | --- | --- | --- |
| ≅ | ∠LNO | ∠MNL | ∠NLM | ∠OLN |
| Statements | Reasons |
| --- | --- |
| | |
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Answer
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Step 1: Recall the Parallelogram Side Theorem and its converse.
The Parallelogram Side Theorem states that if a quadrilateral has opposite sides that are congruent, then it is a parallelogram. The converse of this theorem states that if a quadrilateral is a parallelogram, then its opposite sides are congruent.
Step 2: Understand the given information and the goal.
Given: LM ≅ ON and LO ≅ MN Goal: Prove that LMNO is a parallelogram
Final Answer
Since LM ≅ ON and LO ≅ MN, LMNO is a parallelogram by the Parallelogram Side Theorem converse.
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