Quadrilaterals Flashcards

Quadrilaterals Overview

• A quadrilateral is a four-sided figure.

Types of Quadrilaterals

• Six types of quadrilaterals: square, rhombus, rectangle, kite, trapezoid, and parallelogram.

Sides and Angles

• Sides are line segments joining two vertices.
• Angles can be congruent (90 degrees), consecutive-supplementary, or opposite-congruent.

Parallelogram

• Defined as a quadrilateral with both pairs of opposite sides parallel.

Rhombus

• A type of parallelogram with four congruent sides and opposite equal angles.

Kite

• A quadrilateral with two pairs of consecutive sides congruent, lacking congruent opposite sides.

Trapezoid

• A quadrilateral featuring one pair of parallel sides.

Square

• A quadrilateral characterized by four right angles and four congruent sides; can be seen as a rectangle with equal adjacent sides.

Rectangle

• A parallelogram with four right angles, typically having unequal adjacent sides compared to a square.

Proof Techniques

• Proofs involve logical arguments with statements supported by accepted truths.

Proof for Parallelogram

• If opposite sides or angles are congruent, the quadrilateral is a parallelogram.

Proof for Rhombus

• Demonstrate equal side lengths and that diagonals are perpendicular bisectors of each other; also that diagonals bisect opposite angles.

Proof for Rectangle

• Confirm all angles are 90 degrees, show one pair of sides is parallel, and prove that diagonals bisect each other and are equal.

Proof for Trapezoid

• Involves showing the presence of two parallel sides and congruence of base angles.

Proof for Kite

• Established if two disjoint pairs of consecutive sides are congruent; also, if one diagonal bisects the other perpendicularly.

Proof for Quadrilateral

• Involves creating two pairs of congruent triangles within the quadrilateral.

Proof for Square

• To confirm a quadrilateral is a square, it must have four congruent sides and angles, or two consecutive sides of a rectangle must be equal.

Proof for Isosceles Trapezoid

• Requires proving the presence of two parallel sides with congruent lower and upper bases.

Explore the fundamentals of quadrilaterals with these flashcards. Learn definitions, types, and properties like sides, angles, and diagonals. This quiz is perfect for anyone looking to deepen their understanding of four-sided figures.