https://file.aiquickdraw.com/mathbot/file/1729585970953z2s0lthj.jpg

The question asks which quadrilateral shown could be proved to be a parallelogram by Theorem 6.2E, which states that a quadrilateral with diagonals that bisect each other is a parallelogram.

Let's analyze the figures:

- **ABCD**: The diagonals are not shown, so we cannot verify if they bisect each other.
- **EFGH**: No diagonals are shown.
- **JKLM**: No diagonals are shown.
- **MNOP**: The diagonals are drawn, and we can see that they intersect at the midpoint, suggesting that they bisect each other.
- **QRST**: No diagonals are drawn.

Based on this, the quadrilateral **MNOP** has diagonals that bisect each other. This fits the condition of Theorem 6.2E.

Thus, the answer is **MNOP**.

Would you like further details on why the diagonals bisecting each other prove the quadrilateral is a parallelogram? 

Here are 5 related questions to expand the topic:
1. What are the properties of diagonals in a parallelogram?
2. Can a quadrilateral be a parallelogram if only one diagonal is bisected?
3. What other theorems can be used to prove a quadrilateral is a parallelogram?
4. How can we verify if diagonals bisect each other geometrically?
5. What distinguishes a parallelogram from other quadrilaterals?

**Tip**: In any parallelogram, opposite sides are both parallel and equal in length, and the diagonals bisect each other.

Which quadrilateral shown could be proved to be a parallelogram by Theorem 6.2E (Quad with diagonals that bisect each other)?

This problem explores how to identify a parallelogram using Theorem 6.2E, which states that a quadrilateral with diagonals that bisect each other can be proven to be a parallelogram. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation