Learn on PengiBig Ideas Math, Advanced 2Chapter 12: Constructions and Scale Drawings

Section 12.4: Quadrilaterals

In Section 12.4 of Big Ideas Math Advanced 2, Grade 7 students learn to classify quadrilaterals — including trapezoids, parallelograms, kites, rectangles, rhombuses, and squares — by analyzing properties of their sides and angles. Students explore the hierarchy of quadrilateral types and apply the rule that the sum of interior angle measures of any quadrilateral is 360 degrees. The lesson also covers constructing quadrilaterals using geoboards and geometry software.

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

Classifying Quadrilaterals Using Most Specific Names

Property

When classifying quadrilaterals, always use the most specific name that applies.
Follow the hierarchy: square \rightarrow rectangle/rhombus \rightarrow parallelogram \rightarrow quadrilateral, and kite or trapezoid as separate branches.

Examples

Section 3

Properties of Parallelograms, Rhombuses, Squares, and Kites

Property

A parallelogram has opposite sides parallel and congruent, and opposite angles congruent.
A rhombus is a parallelogram with four congruent sides.
A square is a parallelogram with four congruent sides and four right angles (90°90°).
A kite has two pairs of congruent adjacent sides with diagonals perpendicular to each other.

Examples

Section 4

Properties of Rectangles

Property

  • Rectangles have four sides and four right (9090^\circ) angles.
  • Opposite sides are parallel and equal in length.
  • All four angles are congruent (each measuring 9090^\circ).
  • The diagonals are equal in length and bisect each other.
  • A rectangle is a special type of parallelogram where all angles are right angles.

Examples

Book overview

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Chapter 12: Constructions and Scale Drawings

  1. Lesson 1

    Section 12.1: Adjacent and Vertical Angles

  2. Lesson 2

    Section 12.2: Complementary and Supplementary Angles

  3. Lesson 3

    Section 12.3: Triangles

  4. Lesson 4Current

    Section 12.4: Quadrilaterals

  5. Lesson 5

    Section 12.5: Scale Drawings

Lesson overview

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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

Classifying Quadrilaterals Using Most Specific Names

Property

When classifying quadrilaterals, always use the most specific name that applies.
Follow the hierarchy: square \rightarrow rectangle/rhombus \rightarrow parallelogram \rightarrow quadrilateral, and kite or trapezoid as separate branches.

Examples

Section 3

Properties of Parallelograms, Rhombuses, Squares, and Kites

Property

A parallelogram has opposite sides parallel and congruent, and opposite angles congruent.
A rhombus is a parallelogram with four congruent sides.
A square is a parallelogram with four congruent sides and four right angles (90°90°).
A kite has two pairs of congruent adjacent sides with diagonals perpendicular to each other.

Examples

Section 4

Properties of Rectangles

Property

  • Rectangles have four sides and four right (9090^\circ) angles.
  • Opposite sides are parallel and equal in length.
  • All four angles are congruent (each measuring 9090^\circ).
  • The diagonals are equal in length and bisect each other.
  • A rectangle is a special type of parallelogram where all angles are right angles.

Examples

Book overview

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

Continue this chapter

Chapter 12: Constructions and Scale Drawings

  1. Lesson 1

    Section 12.1: Adjacent and Vertical Angles

  2. Lesson 2

    Section 12.2: Complementary and Supplementary Angles

  3. Lesson 3

    Section 12.3: Triangles

  4. Lesson 4Current

    Section 12.4: Quadrilaterals

  5. Lesson 5

    Section 12.5: Scale Drawings