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Questions and Answers
What is a rectangle?
What is a rectangle?
- A quadrilateral with at least one pair of parallel sides
- A parallelogram with four right angles (correct)
- A parallelogram with all sides equal
- A rectangle with all sides equal and four right angles
What is a rhombus?
What is a rhombus?
- A shape with four right angles
- A quadrilateral with one pair of parallel sides
- A rectangle with all sides equal
- A parallelogram with all sides equal (correct)
What is a square?
What is a square?
- A rectangle with all sides equal (correct)
- A quadrilateral with at least one pair of parallel sides
- A parallelogram with four right angles
- All of the above
What is a trapezoid?
What is a trapezoid?
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Match the vocabulary word with the correct definition:
Match the vocabulary word with the correct definition:
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If a pair of opposite sides of a quadrilateral are parallel and equal, what does it constitute?
If a pair of opposite sides of a quadrilateral are parallel and equal, what does it constitute?
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What can be inferred if the four sides of a quadrilateral are equal?
What can be inferred if the four sides of a quadrilateral are equal?
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A square is __________ a rhombus.
A square is __________ a rhombus.
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Study Notes
Parallelograms and Related Geometric Concepts
- Rectangle: A type of parallelogram characterized by having four right angles.
- Rhombus: Defined as a parallelogram where all four sides are of equal length.
- Square: A specific kind of rectangle, distinguished by having both four right angles and all sides equal.
- Trapezoid: A quadrilateral that has at least one pair of parallel sides.
Vocabulary Matching
- Rectangle: A parallelogram with four right angles.
- Rhombus: A parallelogram with all sides equal.
- Square: A rectangle with all sides equal and four right angles.
- Trapezoid: A quadrilateral with at least one pair of parallel sides.
Proofs in Geometry
- Midpoints of a Rectangle: When joining the midpoints of a rectangle's sides (K, L, M, N), the resulting shape KLMN is a parallelogram because if one pair of opposite sides are parallel and equal in length, the figure is classified as a parallelogram.
- Quadrilateral Being a Rhombus: If a quadrilateral has all four sides equal (AB = BC = CD = DA), it can be proven that the quadrilateral is a rhombus because all quadrilaterals fall under the umbrella of parallelograms.
Rhombus and Square Relationships
- A square is always considered a rhombus because it meets the criterion of having all sides equal.
Lengths and Properties
- In a parallelogram (specifically a rectangle), opposite sides are equal. Therefore, if AB is given, then AB = DC.
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