Quadrilaterals: Classification - Varsity Tutors

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Quadrilaterals: Classification

Study Guide

Key Definition

A quadrilateral is a polygon with four sides. Key types include parallelogram, rectangle, rhombus, and square.

Important Notes

• •A parallelogram has opposite sides parallel and equal
• •Rectangles have four right angles
• •A rhombus has all sides equal
• •Squares combine the properties of rectangles and rhombi
• •Diagonals of a rhombus intersect at right angles

Mathematical Notation

$\angle$ represents an angle$x^2$ means x squared$\sqrt{x}$ represents the square root of x$\cong$ means congruent$\parallel$ indicates parallel linesRemember to use proper notation when solving problems

Why It Works

Parallel sides create congruent corresponding angles, so rectangles have right angles. Rhombi have equal sides, forcing diagonals to intersect at right angles and to bisect the angles. Area formulas come from decomposing quadrilaterals into triangles: for parallelograms and rectangles, A = base × height; for trapezoids, A = ½ (b₁ + b₂) × height; and for rhombi, A = (d₁ × d₂) / 2.

Remember

The diagonals of a rectangle are congruent and bisect each other.

Quick Reference

Parallelogram:Opposite sides and angles are equalRectangle:All angles are $90^\circ$Rhombus:All sides are equal, diagonals intersect at $90^\circ$Square:All properties of a rectangle and a rhombus

Understanding Quadrilaterals: Classification

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Beginner Explanation

Basic explanation: A quadrilateral is a four-sided polygon. Key types:- Parallelogram: opposite sides parallel and equal; area = base × height. Example: base 5, height 3 → area 15.- Rectangle: four right angles; area = length × width. Example: 3 × 4 = 12.- Rhombus: all sides equal; area = base × height. - Square: all sides equal and all angles 90°; area = side².Now showing Beginner level explanation.

Practice Problems

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1

Quick Quiz

Single Choice QuizBeginner

Which statement is always true for a rectangle?

A$\angle\text{ is }90^\circ$BDiagonals intersect at $90^\circ$CAll sides are equalDNone of the aboveCheck AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

Imagine you are designing a rectangular garden. If the diagonals are $10 \text{ meters}$ long and the width is $6 \text{ meters}$, what is the garden's area?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

If a rhombus has an angle of $60^\circ$, what are the measures of the other angles?

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

In a trapezoid, one pair of opposite sides is $\parallel$. If the bases are $8 \text{ units}$ and $12 \text{ units}$ and the height is $5 \text{ units}$, what is the area?

A$20 \text{ units}^2$B$30 \text{ units}^2$C$40 \text{ units}^2$D$50 \text{ units}^2$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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