Math Problem Statement
Solution
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:
- What are the properties of diagonals in a parallelogram?
- Can a quadrilateral be a parallelogram if only one diagonal is bisected?
- What other theorems can be used to prove a quadrilateral is a parallelogram?
- How can we verify if diagonals bisect each other geometrically?
- 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.
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Math Problem Analysis
Mathematical Concepts
Geometry
Quadrilaterals
Parallelograms
Diagonals
Formulas
-
Theorems
Theorem 6.2E
Suitable Grade Level
Grades 8-10
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