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Made Easy Does anyone want to classify my figure? Figur es Two- Dimensional Classif ying ©Mike’s Math Mall

Does anyone want to classify my figure? ©Mike’s Math Mall

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Page 1: Does anyone want to classify my figure? ©Mike’s Math Mall

Made Easy

Does anyonewant to classify my

figure?

Figures

Two-Dimensional

Classifying

©Mike’s Math Mall

Page 2: Does anyone want to classify my figure? ©Mike’s Math Mall

Classifying 2-Dimensional FiguresIn life, we like to group objects incategories based on their properties.

Placing objects into categories makes it easier to compare them with other objects.

I strugglewith this junk all

the time!

Really? How so?

I’m always wondering…can

a soft taco be grouped with a burrito?

Or is aquesadilla just a smashed burrito

sandwich?

I feel your pain?

Page 3: Does anyone want to classify my figure? ©Mike’s Math Mall

Classifying 2-Dimensional FiguresLet’s look at some vocabulary

terms before we start classifying figures.

Two-dimensional – having a width and a height but flat like a piece of paper.

One-dimension

Two-dimensions

Three-dimensionsPolygon – a two-dimensional shape made up of straight lines that are closed.

Polygon

Page 4: Does anyone want to classify my figure? ©Mike’s Math Mall

Classifying 2-Dimensional FiguresHere is a list of the most basic polygons:

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

3-sided

4-sided

5-sided

6-sided

7-sided

8-sided

Page 5: Does anyone want to classify my figure? ©Mike’s Math Mall

Classifying 2-Dimensional FiguresPolygons are either regular or irregular.

This is a regular pentagon because ALL of its sides and angles are congruent.

Congruent – having the same measure

This is an irregular pentagon because some of its sides and anglesare not congruent.

Hash marks indicate sides with the same length.Angle arcs indicate angles of the same measure.

Page 6: Does anyone want to classify my figure? ©Mike’s Math Mall

Triangle

s

Classifyi

ng

Yep!I got it on

sale!

Part I

Page 7: Does anyone want to classify my figure? ©Mike’s Math Mall

Properties of TrianglesAll triangles have:

3 sides 3 interior angles (that add up to 180°)

Yeah, butaren’t there like a

bazillion different kinds of triangles?

I wouldn’t say a bazillion!

There are just a few basic ways that we classify or name

triangles!

Just a few?

Why, are we counting?

One mustknow what one is getting into before

one gets into it, Professor!

Just check this out!

Page 8: Does anyone want to classify my figure? ©Mike’s Math Mall

We classify or name triangles by their angles.

Classifying Triangles

Acute Triangle All angles less than 90°

Obtuse Triangle One angle greater

than 90°

< 90°All angles

□One 90° angle

One angle > 90°

Right Triangle One 90° angle

“□” means 90°

Page 9: Does anyone want to classify my figure? ©Mike’s Math Mall

Classifying Triangles

We also classify triangles bytheir side lengths and angle measures.

Equilateral Triangle 3 congruent sides All angles congruent

Isosceles Triangle 2 congruent sides 2 congruent angles

Scalene Triangle No congruent sides No congruent angles

Page 10: Does anyone want to classify my figure? ©Mike’s Math Mall

Name that Triangle!

Classify each triangle by ALL names that apply.

1.

____________________

____________________

3.

140°

____________________

____________________

RightIsosceles

AcuteIsosceles

ObtuseScalene

2.

____________________

____________________

Page 11: Does anyone want to classify my figure? ©Mike’s Math Mall

Classifying Triangles

This doesn’tseem too rough, but

I’ve never seen a cute triangle?

That’s not what “acute” actually

means!

Maybe we should just go take a look at some quadrilaterals now!

It’s nothing personal. I simply

find triangles fairly unattractive.

I’m not paid enough!

Are they cute?

So, what do think about classifying triangles, Mr. Sparkles?

Page 12: Does anyone want to classify my figure? ©Mike’s Math Mall

Quadrilater

als

Classifyi

ng

Part II

I knowwhat you’re thinking…

sweet lid, right?

Page 13: Does anyone want to classify my figure? ©Mike’s Math Mall

Properties of Quadrilaterals

Another main group of polygons arethe quadrilaterals.

All quadrilaterals have: 4 sides 4 interior angles (that add up to 360°)

How can Iclassify these things when I

don’t even know what a cordlaratamal is?

Have you ever heard of a square?

Yeah, duh!

Well, squares arequad-ri-lat-er-als!

Justchecking tosee if you’re

awake!

Page 14: Does anyone want to classify my figure? ©Mike’s Math Mall

Classifying QuadrilateralsLet’s classify quadrilaterals from those with the

fewest properties to those with the most properties.

Basic Quadrilateral 4-sided polygon

Trapezoid Quadrilateral with one

pair of parallel sides

Parallel Lines – Two lines on the same plane that will never cross. They are always the same distance apart.

Page 15: Does anyone want to classify my figure? ©Mike’s Math Mall

Classifying QuadrilateralsParallelogram

Two pairs of parallel sides Opposite sides congruent

Rectangle A parallelogram Four 90° angles

□ □

□ □

By definition, rectangles are considered parallelograms.Why can’t parallelograms be classified as rectangles?

Parallelograms do not have 4 congruent angles.

Page 16: Does anyone want to classify my figure? ©Mike’s Math Mall

Classifying QuadrilateralsRhombus

A parallelogram 4 congruent sides

Square A parallelogram A rectangle A rhombus

□ □

Why can we classify a square as a rectangle and a rhombus?A square is a parallelogram with 4 right angles (rectangle)

A square is a parallelogram with 4 congruent sides (rhombus)

Page 17: Does anyone want to classify my figure? ©Mike’s Math Mall

Name each of the following polygons.

YIELD

ITALIA

World Cup 2014

WORD BANKequilateral trianglepentagonrectangleparallelogramright triangleoctagontrapezoidsquarerhombus

Higher Grounds

Coffee

1.

2.

FFA

Future Farmers of America

3.WorkZone

4.

5.

Trail 36.

trapezoid

equi

late

ral

tria

ngle

parallelogram

pentagon

right triangle

trapezoid

Classifying 2-Dimensional Figures

Page 18: Does anyone want to classify my figure? ©Mike’s Math Mall

Answer the following questions.

Classifying 2-Dimensional Figures

1. What do the “hash marks” indicate on the sides of polygons?

2. What’s the difference between a regular and irregular polygon?

3. By definition, we can classify all rectangles as parallelograms, but why can’t we classify parallelograms as rectangles?

4. What’s the difference between an obtuse angle and an acute angle?

Hash marks indicate that those side lengths are congruent.

A regular polygon has sides and angles that are all congruent. An irregular polygon does not.

A rectangle has two pairs of parallel sides and two pairs of congruent sides as defined by a parallelogram. However, a rectangle has four 90° right angles which is not included in the definition of a parallelogram.

An obtuse angle is greater than 90°, and an acute angle is less than 90°.

Page 19: Does anyone want to classify my figure? ©Mike’s Math Mall

Match each term with one of the figures.

1. Scalene Obtuse Triangle _____ 2. Rhombus _____ 3. Regular Pentagon _____

4. Trapezoid _____ 5. Isosceles Triangle _____ 6. Equilateral Triangle_____

7. Octagon _____ 8. Parallelogram _____ 9. Irregular Quadrilateral _____

120°

A

B

C

D

E

F

GH

I

Classifying 2-Dimensional Figures

H G F

A B I

E C D

Page 20: Does anyone want to classify my figure? ©Mike’s Math Mall

Classifying Quadrilaterals

So how do you feel about classifying two-dimensional figures, Sparky?

I am aclassifying polygaterals

and quadrigonialsbeast, sir!

I’m not sure you…

I’ll proveit! Ask me aquestion!

Ok! How many sides does a heptagon have?

That’s easy!Extinct dinosaurs

don’t have anysides!

Promise me you’ll look over the notes!

©Mike’s Math Mall

It’s apromise,

sir!