1. want to classify my figure?
Does anyone
want to classify my figure?
Classifying
Two-Dimensional
Figures
Made Easy
©Mike’s Math Mall

2. Classifying 2-Dimensional Figures
In life, we like to group objects in
categories based on their properties.
Placing objects into categories makes it easier to compare them with other objects.
I’m always wondering…can
a soft taco be grouped with a burrito?
I feel your pain?
I struggle
with this junk all the time!
Or is a
quesadilla just a smashed burrito
sandwich?
Really? How so?

3. Classifying 2-Dimensional Figures
Let’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.
Polygon
Two-dimensions
Polygon – a two-dimensional shape made up of straight lines that are closed.
One-dimension
Three-dimensions

4. Here is a list of the most basic polygons:
Classifying 2-Dimensional Figures
Here is a list of the most basic polygons:
Triangle
3-sided
Hexagon
6-sided
Quadrilateral
4-sided
Heptagon
7-sided
Pentagon
5-sided
Octagon
8-sided

5. Polygons are either regular or irregular.
Classifying 2-Dimensional Figures
Polygons are either regular or irregular.
This is a regular pentagon because ALL of its sides and angles are congruent.
Congruent – having the same measure
Hash marks indicate sides with the same length.
Angle arcs indicate angles of the same measure.
This is an irregular pentagon because some of its sides and angles
are not congruent.

6. Part I
Classifying
Triangles
Yep!
I got it on
sale!

7. Properties of Triangles
All triangles have:
3 sides
3 interior angles (that add up to 180°)
Yeah, but
aren’t there like a bazillion different kinds of triangles?
Just a few?
One must
know what one is getting into before one gets into it, Professor!
I wouldn’t say a bazillion!
Why, are we counting?
There are just a few basic ways that we classify or name triangles!
Just check this out!

8. We classify or name triangles by their angles.
Classifying Triangles
We classify or name triangles by their angles.
< 90°
All angles
Acute Triangle
All angles less than 90°
Right Triangle
One 90° angle
“□” means 90° □
One 90° angle
Obtuse Triangle
One angle greater than 90°
One angle > 90°

9. We also classify triangles by their side lengths and angle measures.
Classifying Triangles
We also classify triangles by
their 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

10. Classify each triangle by ALL names that apply.
Name that Triangle!
Classify each triangle by ALL names that apply. 2.
____________________
Acute
Isosceles □ 1.
____________________ 3.
140°
____________________
Right
Isosceles
Obtuse
Scalene

11. So, what do think about classifying triangles, Mr. Sparkles?
It’s nothing personal. I simply find triangles fairly unattractive.
This doesn’t
seem too rough, but
I’ve never seen a cute triangle?
Are they cute?
That’s not what “acute” actually means!
I’m not paid enough!
Maybe we should just go take a look at some quadrilaterals now!

12. Quadrilaterals Classifying Part II I know what you’re thinking…
sweet lid, right?

13. Another main group of polygons are
Properties of Quadrilaterals
Another main group of polygons are
the quadrilaterals.
All quadrilaterals have:
4 sides
4 interior angles (that add up to 360°)
How can I
classify these things when I don’t even know what a cordlaratamal is?
Yeah, duh!
Just
checking to
see if you’re awake!
Have you ever heard of a square?
Well, squares are
quad-ri-lat-er-als!

14. Classifying Quadrilaterals
Let’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.

15. Classifying Quadrilaterals
Parallelogram
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.

16. Classifying Quadrilaterals
Square
A parallelogram
A rectangle
A rhombus
Rhombus
A parallelogram
4 congruent sides □ □ □ □
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)

17. Trail 3 Classifying 2-Dimensional Figures Higher Grounds ITALIA Work F
Name each of the following polygons. 2.
YIELD
WORD BANK
equilateral triangle
pentagon
rectangle
parallelogram
right triangle
octagon
trapezoid
square
rhombus
Higher Grounds
Coffee 1.
trapezoid
equilateral
triangle
parallelogram
Work
Zone 4. F FA
Future Farmers
of America 3.
pentagon 5.
ITALIA
World Cup
2014
Trail 3 6.
trapezoid
right triangle

18. Classifying 2-Dimensional Figures
Answer the following questions.
1. What do the “hash marks” indicate on the sides of polygons?
Hash marks indicate that those side lengths are congruent.
2. What’s the difference between a regular and irregular polygon?
A regular polygon has sides and angles that are all congruent. An irregular polygon does not.
3. By definition, we can classify all rectangles as parallelograms, but why can’t we classify parallelograms as rectangles?
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.
4. What’s the difference between an obtuse angle and an acute angle?
An obtuse angle is greater than 90°, and an acute angle is less than 90°.

19. Classifying 2-Dimensional Figures
Match each term with one of the figures.
1. Scalene Obtuse Triangle _____ Rhombus _____ Regular Pentagon _____ H G F
4. Trapezoid _____ Isosceles Triangle _____ Equilateral Triangle_____ A B I
7. Octagon _____ Parallelogram _____ Irregular Quadrilateral _____ E C D I A E F C D B
120° G H

20. So how do you feel about classifying two-dimensional figures, Sparky?
Classifying Quadrilaterals
So how do you feel about classifying two-dimensional figures, Sparky?
I’ll prove
it! Ask me a
question!
I am a
classifying polygaterals and quadrigonials
beast, sir!
It’s a
promise,
sir!
That’s easy!
Extinct dinosaurs
don’t have any
sides!
I’m not sure you…
Promise me you’ll look over the notes!
Ok! How many sides does a heptagon have?
©Mike’s Math Mall