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Classify Shapes in a Hierarchy (Quadrilaterals & Triangles)
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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!
This video was just released 07/26/2021.
Lesson materials will follow about 1 week later.
- Discussion Questions
Before Video
What does the measurement of an angle tell you?ANSWERIt tells you the size of the turn, or amount or rotation between the two adjacent lines, rays, or line segments.
It means that one side of the shape is a mirror image of the other.
The tracks are parallel because they continue on without ever getting closer to one another, or farther apart.
The railway ties are perpendicular to the tracks because they cross at a 90° angle.
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?ANSWERIt means that a parallelogram has all the properties of a quadrilateral, plus the properties specific to parallelograms.
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.
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.
(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.
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
A characteristic that is true of a geometric shape in a given category.
- Category DEFINE
A classification of shapes with a defined set of properties.
- Polygon DEFINE
A closed shape with all straight sides.
- Angle DEFINE
A measurement of the rotation between two lines with a common endpoint.
- Right Angle DEFINE
An angle that measures 90°.
- Acute Angle DEFINE
An angle that measures between 0° and 90°.
- Obtuse Angle DEFINE
An angle that measures between 90° and 180°.
- Triangle DEFINE
A three-sided polygon.
- Equilateral Triangle DEFINE
A triangle where all sides have an equal length.
- Isosceles Triangle DEFINE
A triangle with two equal sides.
- Scalene Triangle DEFINE
A triangle with no sides the same length.
- Quadrilateral DEFINE
A four-sided polygon.
- Parallelogram DEFINE
A quadrilateral with two sets of parallel sides.
- Hierarchy DEFINE
A categorization method where things are sorted into more and more specific groups, and the subgroups retain all the properties of the supergroup.
- Supergroup DEFINE
A group that can be divided into smaller subgroups based on a property of the items you are sorting.
- Subgroup DEFINE
A group with a more specific property than the supergroup. For example, of the supergroup “all US states,” there is a subgroup “states on the West coast.”
- Rectangle DEFINE
A parallelogram with all right angles.
- Rhombus DEFINE
A quadrilateral with 4 equal sides and two pairs of parallel sides.
- Trapezoid (inclusive) DEFINE
A quadrilateral with at least one set of parallel sides.
- Trapezoid (exclusive) DEFINE
A quadrilateral with exactly one pair of parallel sides.
- Pentagon DEFINE
A five-sided polygon.
- Hexagon DEFINE
A six-sided polygon.
- Heptagon DEFINE
A seven-sided polygon.
- Octagon DEFINE
An eight-sided polygon.
- Nonagon DEFINE
A nine-sided polygon.
- Property DEFINE
- Practice Word Problems
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Level 1
What are the hierarchical categories for a three-sided shape with an obtuse angle and no equal side lengths?
Level 2
Is a square also a rhombus? Is it also a rectangle?
Level 3
What hierarchical categories does a rectangle belong to?