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Made Easy
Does anyonewant to classify my
figure?
Figures
Two-Dimensional
Classifying
©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?
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
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
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.
Triangle
s
Classifyi
ng
Yep!I got it on
sale!
Part I
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!
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°
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
Name that Triangle!
Classify each triangle by ALL names that apply.
□
1.
____________________
____________________
3.
140°
____________________
____________________
RightIsosceles
AcuteIsosceles
ObtuseScalene
2.
____________________
____________________
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?
Quadrilater
als
Classifyi
ng
Part II
I knowwhat you’re thinking…
sweet lid, right?
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!
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.
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.
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)
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
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°.
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
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!