Learn on PengiIllustrative Mathematics, Grade 5Chapter 7: Shapes on the Coordinate Plane

Lesson 4: Hierarchy of Quadrilaterals

In this Grade 5 Illustrative Mathematics lesson, students explore the hierarchy of quadrilaterals by examining how categories such as parallelograms, rectangles, rhombuses, and squares relate to and nest within one another. Students use shared attributes to classify shapes and understand why a square, for example, belongs to multiple categories simultaneously. This lesson builds geometric reasoning skills aligned with the properties and classification of two-dimensional figures.

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.

Book overview

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Chapter 7: Shapes on the Coordinate Plane

  1. Lesson 1

    Lesson 1: Explore and Plot Points on Coordinate Grid

  2. Lesson 2

    Lesson 2: Plot More Points

  3. Lesson 3

    Lesson 3: Classify Quadrilaterals

  4. Lesson 4Current

    Lesson 4: Hierarchy of Quadrilaterals

  5. Lesson 5

    Lesson 5: Rectangles and Squares

  6. Lesson 6

    Lesson 6: Sort Triangles

  7. Lesson 7

    Lesson 7: Patterns and Relationships

  8. Lesson 8

    Lesson 8: Patterns and Ordered Pairs

  9. Lesson 9

    Lesson 9: Represent Problems on the Coordinate Grid

  10. Lesson 10

    Lesson 10: Perimeter and Area of Rectangles

Lesson overview

Expand to review the lesson summary and core properties.

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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.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 7: Shapes on the Coordinate Plane

  1. Lesson 1

    Lesson 1: Explore and Plot Points on Coordinate Grid

  2. Lesson 2

    Lesson 2: Plot More Points

  3. Lesson 3

    Lesson 3: Classify Quadrilaterals

  4. Lesson 4Current

    Lesson 4: Hierarchy of Quadrilaterals

  5. Lesson 5

    Lesson 5: Rectangles and Squares

  6. Lesson 6

    Lesson 6: Sort Triangles

  7. Lesson 7

    Lesson 7: Patterns and Relationships

  8. Lesson 8

    Lesson 8: Patterns and Ordered Pairs

  9. Lesson 9

    Lesson 9: Represent Problems on the Coordinate Grid

  10. Lesson 10

    Lesson 10: Perimeter and Area of Rectangles