Learn on PengiBig Ideas Math, Course 2Chapter 7: Constructions and Scale Drawings

Lesson 4: Quadrilaterals

In this Grade 7 lesson from Big Ideas Math, Course 2, Chapter 7, students learn to classify quadrilaterals — including trapezoids, parallelograms, kites, rectangles, rhombuses, and squares — based on properties of their sides and angles. Students also apply the rule that the sum of interior angle measures of any quadrilateral equals 360° to find missing angle measures. Hands-on activities using geoboards and geometry software reinforce how these shapes are defined and related to one another.

Section 1

Defining a Quadrilateral

Property

A quadrilateral is a polygon with exactly four sides and four vertices.
The sum of all interior angles in any quadrilateral equals 360°360°:

∠A+∠B+∠C+∠D=360°\angle A + \angle B + \angle C + \angle D = 360°

Examples

Section 2

Types of Quadrilaterals

Property

  • A quadrilateral is a polygon with four sides.
  • A trapezoid is a quadrilateral with one pair of parallel sides.
  • A parallelogram is a quadrilateral with both pairs of opposing sides parallel.
  • A rhombus is a parallelogram with all sides of the same length.
  • A kite is a quadrilateral with two pairs of adjacent sides of the same lengths.
  • A rectangle is a parallelogram with at least one right angle.
  • A square is a rectangle with all sides of the same length.

Examples

  • A garden plot has four sides, with opposite sides parallel and all corners forming right angles. This shape is a rectangle.
  • A kite has two short sides of equal length next to each other, and two long sides of equal length next to each other. This follows the definition of a kite.
  • A slice of cheese is a quadrilateral with only one pair of parallel sides. This makes it a trapezoid.

Explanation

Think of these shapes like a family tree! A square is a special type of rectangle, which is a special type of parallelogram. Each shape inherits traits from the one above it but adds its own unique rule.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Defining a Quadrilateral

Property

A quadrilateral is a polygon with exactly four sides and four vertices.
The sum of all interior angles in any quadrilateral equals 360°360°:

∠A+∠B+∠C+∠D=360°\angle A + \angle B + \angle C + \angle D = 360°

Examples

Section 2

Types of Quadrilaterals

Property

  • A quadrilateral is a polygon with four sides.
  • A trapezoid is a quadrilateral with one pair of parallel sides.
  • A parallelogram is a quadrilateral with both pairs of opposing sides parallel.
  • A rhombus is a parallelogram with all sides of the same length.
  • A kite is a quadrilateral with two pairs of adjacent sides of the same lengths.
  • A rectangle is a parallelogram with at least one right angle.
  • A square is a rectangle with all sides of the same length.

Examples

  • A garden plot has four sides, with opposite sides parallel and all corners forming right angles. This shape is a rectangle.
  • A kite has two short sides of equal length next to each other, and two long sides of equal length next to each other. This follows the definition of a kite.
  • A slice of cheese is a quadrilateral with only one pair of parallel sides. This makes it a trapezoid.

Explanation

Think of these shapes like a family tree! A square is a special type of rectangle, which is a special type of parallelogram. Each shape inherits traits from the one above it but adds its own unique rule.