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Question

Difficulty: EasyProperties of Quadrilaterals

A geometry student claims that every rectangle is also a parallelogram. Is this claim true or false?

Answer: Answer

Answer

True
The claim is true because a rectangle must have four right angles, which mathematically forces opposite sides to be parallel, thereby meeting the definition of a parallelogram.

Step-by-Step Solution

1
Define a rectangle based on its angle properties.
A rectangle is a quadrilateral with four right angles.
This is the primary defining characteristic of a rectangle.
2
Define a parallelogram based on its side properties.
A parallelogram is a quadrilateral with two pairs of parallel opposite sides.
This is the primary defining characteristic of a parallelogram.
3
Analyze the relationship between the two definitions.
In a quadrilateral with four 90∘90^\circ angles, consecutive angles sum to 180∘180^\circ. By the consecutive interior angles converse, the opposite sides are parallel. Since both pairs of opposite sides are parallel, the quadrilateral must be a parallelogram. Thus, every rectangle is a parallelogram.
To determine whether the student's statement is correct.

Key Concept

Hierarchical classification of quadrilaterals
Estimated Time:30s
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Topics

Properties of Quadrilaterals

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