Geometry Parallelograms Flashcards

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.