Learn on PengiSaxon Math, Course 2Chapter 6: Lessons 51-60, Investigation 6

Investigation 6: Classifying Quadrilaterals

In this Grade 7 lesson from Saxon Math Course 2, students learn to classify quadrilaterals by analyzing properties such as parallel sides, equal side lengths, and right angles, distinguishing between parallelograms, trapezoids, trapeziums, rectangles, rhombuses, and kites. Students use Venn diagrams to explore the hierarchical relationships among these shapes, including how a square is simultaneously a rectangle, a rhombus, and a parallelogram. The investigation also covers lines of symmetry for special quadrilaterals and compares perimeter and area when a rectangle is transformed into a parallelogram.

Section 1

📘 Classifying Quadrilaterals

New Concept

A quadrilateral with two pairs of parallel sides is a parallelogram.

Why it matters

Mastering the classification of shapes teaches you the language of geometric logic, allowing you to break down complex problems into simpler, known components. This skill of sorting by properties is the same foundational thinking used in advanced fields like computer science and data analysis.

What’s next

Next, you’ll apply these definitions to sort various quadrilaterals and explore their unique properties and symmetries.

Section 2

Parallelogram

Property

A quadrilateral with two pairs of parallel sides.

Examples

A square is a parallelogram with four equal sides and four 90∘90^\circ angles.
A rhombus with side length 5 is a parallelogram where all sides are equal.

Explanation

Think of a rectangle that's been pushed over! Its opposite sides stay parallel and equal, but the angles aren't necessarily perfect right angles anymore. It's a shape that loves to lean while keeping its opposite sides perfectly aligned, just like a disciplined dancer mid-pose.

Section 3

Trapezoid

Property

A quadrilateral with just one pair of parallel sides.

Examples

A shape with parallel bases of lengths 4 cm and 9 cm.
An isosceles trapezoid has equal non-parallel sides and a line of symmetry.

Explanation

Imagine a table where the top and bottom edges are parallel, but the legs slant outwards. That’s a trapezoid! It’s the unique quadrilateral that commits to having only one pair of parallel sides, which are called its bases. It’s the rebel of the quadrilateral family.

Section 4

Rhombus

Property

A rhombus is a parallelogram where all four sides have equal length.

Examples

A square is a special rhombus with four right angles.
A quadrilateral with four sides of length 8 cm is a rhombus.

Explanation

Imagine a square that got pushed over. The sides are still equal, but the angles are not necessarily 90∘90^\circ. It's the classic diamond shape you see on playing cards! It's basically a tilted square, adding a little bit of flair to the quadrilateral world.

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Chapter 6: Lessons 51-60, Investigation 6

  1. Lesson 1

    Lesson 51: Scientific Notation for Large Numbers

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  2. Lesson 2

    Lesson 52: Order of Operations

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  3. Lesson 3

    Lesson 53: Ratio Word Problems

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  4. Lesson 4

    Lesson 54: Rate Word Problems

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  5. Lesson 5

    Lesson 55: Average and Rate Problems with Multiple Steps

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  6. Lesson 6

    Lesson 56: Plotting Functions

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  7. Lesson 7

    Lesson 57: Negative Exponents, Scientific Notation for Small Numbers

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  8. Lesson 8

    Lesson 58: Symmetry

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  9. Lesson 9

    Lesson 59: Adding Integers on the Number Line

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  10. Lesson 10

    Lesson 60: Fractional Part of a Number, Part 1, Percent of a Number, Part 1

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  11. Lesson 11Current

    Investigation 6: Classifying Quadrilaterals

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Lesson overview

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Section 1

📘 Classifying Quadrilaterals

New Concept

A quadrilateral with two pairs of parallel sides is a parallelogram.

Why it matters

Mastering the classification of shapes teaches you the language of geometric logic, allowing you to break down complex problems into simpler, known components. This skill of sorting by properties is the same foundational thinking used in advanced fields like computer science and data analysis.

What’s next

Next, you’ll apply these definitions to sort various quadrilaterals and explore their unique properties and symmetries.

Section 2

Parallelogram

Property

A quadrilateral with two pairs of parallel sides.

Examples

A square is a parallelogram with four equal sides and four 90∘90^\circ angles.
A rhombus with side length 5 is a parallelogram where all sides are equal.

Explanation

Think of a rectangle that's been pushed over! Its opposite sides stay parallel and equal, but the angles aren't necessarily perfect right angles anymore. It's a shape that loves to lean while keeping its opposite sides perfectly aligned, just like a disciplined dancer mid-pose.

Section 3

Trapezoid

Property

A quadrilateral with just one pair of parallel sides.

Examples

A shape with parallel bases of lengths 4 cm and 9 cm.
An isosceles trapezoid has equal non-parallel sides and a line of symmetry.

Explanation

Imagine a table where the top and bottom edges are parallel, but the legs slant outwards. That’s a trapezoid! It’s the unique quadrilateral that commits to having only one pair of parallel sides, which are called its bases. It’s the rebel of the quadrilateral family.

Section 4

Rhombus

Property

A rhombus is a parallelogram where all four sides have equal length.

Examples

A square is a special rhombus with four right angles.
A quadrilateral with four sides of length 8 cm is a rhombus.

Explanation

Imagine a square that got pushed over. The sides are still equal, but the angles are not necessarily 90∘90^\circ. It's the classic diamond shape you see on playing cards! It's basically a tilted square, adding a little bit of flair to the quadrilateral world.

Book overview

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

Continue this chapter

Chapter 6: Lessons 51-60, Investigation 6

  1. Lesson 1

    Lesson 51: Scientific Notation for Large Numbers

    LearnPractice
  2. Lesson 2

    Lesson 52: Order of Operations

    LearnPractice
  3. Lesson 3

    Lesson 53: Ratio Word Problems

    LearnPractice
  4. Lesson 4

    Lesson 54: Rate Word Problems

    LearnPractice
  5. Lesson 5

    Lesson 55: Average and Rate Problems with Multiple Steps

    LearnPractice
  6. Lesson 6

    Lesson 56: Plotting Functions

    LearnPractice
  7. Lesson 7

    Lesson 57: Negative Exponents, Scientific Notation for Small Numbers

    LearnPractice
  8. Lesson 8

    Lesson 58: Symmetry

    LearnPractice
  9. Lesson 9

    Lesson 59: Adding Integers on the Number Line

    LearnPractice
  10. Lesson 10

    Lesson 60: Fractional Part of a Number, Part 1, Percent of a Number, Part 1

    LearnPractice
  11. Lesson 11Current

    Investigation 6: Classifying Quadrilaterals

    LearnPractice