What does the measurement of an angle tell you?

It tells you the size of the turn, or amount or rotation between the two adjacent lines, rays, or line segments.

What does it mean for something to be symmetrical?

It means that one side of the shape is a mirror image of the other.

Are the two rails on train tracks parallel or perpendicular?

The tracks are parallel because they continue on without ever getting closer to one another, or farther apart.

Are railway ties (the wooden pieces that go underneath the train tracks) parallel or perpendicular to the rails?

The railway ties are perpendicular to the tracks because they cross at a 90° angle.

What does it mean for a shape to be closed?

A closed shape has all of the edges connecting at endpoints, so there are no gaps in the perimeter (distance around the outside of a shape). A closed shape has area.

What does it mean for parallelogram to be a subgroup of quadrilateral?

It means that a parallelogram has all the properties of a quadrilateral, plus the properties specific to parallelograms.

Why is a square both a parallelogram and a kite?

The square inherits the properties of the kite (two sets of adjacent sides with equal length) through the rhombus (four equal sides), and the properties of the parallelogram (two sets of parallel sides) through the rectangle (all right angles). Because the square keeps the properties that define its supergroups, a square is also a parallelogram and a kite.

Can a triangle be a quadrilateral? Explain.

No. A triangle and a quadrilateral are both classified on the property of “number of sides.” A triangle is a shape with exactly three sides, and a quadrilateral is a shape with exactly four sides. This means that a shape cannot be both a triangle and a quadrilateral.

Is a parallelogram a trapezoid? Explain

(Exclusive definition) No. A trapezoid is a shape with exactly one set of parallel sides, so a parallelogram cannot be a trapezoid. (Inclusive definition) Yes. A trapezoid is a shape with at least one set of parallel sides, so parallelogram is a subgroup of trapezoid.

How would you define a hierarchy?

A hierarchy is a system of classification based on sets of properties that become more and more specific as you move down the hierarchy. All subgroups retain all the properties of their supergroups, so in geometry, shapes inherit the properties of the categories above them in the hierarchy.

Classify Shapes in a Hierarchy (Quadrilaterals & Triangles)

LESSON MATERIALS move

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What you will learn from this videoWhat you will learn

How to classify quadrilaterals in a hierarchy based on their attributes.
We’ll also learn how to classify triangles in a hierarchy.
And we will see that this knowledge can help us pack for summer camp and even plan a party!

Discussion Questions
- Before Video
  What does the measurement of an angle tell you?ANSWER
  - It tells you the size of the turn, or amount or rotation between the two adjacent lines, rays, or line segments.
  What does it mean for something to be symmetrical?ANSWER
  - It means that one side of the shape is a mirror image of the other.
  Are the two rails on train tracks parallel or perpendicular?ANSWER
  - The tracks are parallel because they continue on without ever getting closer to one another, or farther apart.
  Are railway ties (the wooden pieces that go underneath the train tracks) parallel or perpendicular to the rails?ANSWER
  - The railway ties are perpendicular to the tracks because they cross at a 90° angle.
  What does it mean for a shape to be closed?ANSWER
  - A closed shape has all of the edges connecting at endpoints, so there are no gaps in the perimeter (distance around the outside of a shape). A closed shape has area.
- After Video
  What does it mean for parallelogram to be a subgroup of quadrilateral?ANSWER
  - It means that a parallelogram has all the properties of a quadrilateral, plus the properties specific to parallelograms.
  Why is a square both a parallelogram and a kite?ANSWER
  - The square inherits the properties of the kite (two sets of adjacent sides with equal length) through the rhombus (four equal sides), and the properties of the parallelogram (two sets of parallel sides) through the rectangle (all right angles). Because the square keeps the properties that define its supergroups, a square is also a parallelogram and a kite.
  Can a triangle be a quadrilateral? Explain.ANSWER
  - No. A triangle and a quadrilateral are both classified on the property of “number of sides.” A triangle is a shape with exactly three sides, and a quadrilateral is a shape with exactly four sides. This means that a shape cannot be both a triangle and a quadrilateral.
  Is a parallelogram a trapezoid? ExplainANSWER
  - (Exclusive definition) No. A trapezoid is a shape with exactly one set of parallel sides, so a parallelogram cannot be a trapezoid. (Inclusive definition) Yes. A trapezoid is a shape with at least one set of parallel sides, so parallelogram is a subgroup of trapezoid.
  How would you define a hierarchy?ANSWER
  - A hierarchy is a system of classification based on sets of properties that become more and more specific as you move down the hierarchy. All subgroups retain all the properties of their supergroups, so in geometry, shapes inherit the properties of the categories above them in the hierarchy.
Vocabulary
- Property DEFINE
- Category DEFINE
- Polygon DEFINE
- Angle DEFINE
- Right Angle DEFINE
- Acute Angle DEFINE
- Obtuse Angle DEFINE
- Triangle DEFINE
- Equilateral Triangle DEFINE
- Isosceles Triangle DEFINE
- Scalene Triangle DEFINE
- Quadrilateral DEFINE
- Parallelogram DEFINE
- Hierarchy DEFINE
- Supergroup DEFINE
- Subgroup DEFINE
- Rectangle DEFINE
- Rhombus DEFINE
- Trapezoid (inclusive) DEFINE
- Trapezoid (exclusive) DEFINE
- Pentagon DEFINE
- Hexagon DEFINE
- Heptagon DEFINE
- Octagon DEFINE
- Nonagon DEFINE
Reading Material
Practice Word Problems
Practice Number Problems
Lesson Plan
Teacher Guide
Assessment
Online Quiz Game Quiz PDF Exit Ticket