QQuestionMathematics
QuestionMathematics
# 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 |
| --- | --- |
| | |
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
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
Step 3:: Apply the Parallelogram Side Theorem converse.
To prove that LMNO is a parallelogram, we need to show that its opposite sides are congruent. We are given that LM ≅ ON and LO ≅ MN. Since these are opposite sides of the quadrilateral, we can directly apply the Parallelogram Side Theorem converse to conclude that LMNO is a parallelogram.
Final Answer
Since LM ≅ ON and LO ≅ MN, LMNO is a parallelogram by the Parallelogram Side Theorem converse.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students