Transcript Document

Does anyone
want to classify my
figure?
©Mike’s Math Mall
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 struggle
with this junk all
the time!
Really?
How so?
I’m always
wondering…can
a soft taco be grouped
with a burrito?
Or is a
quesadilla just a
smashed burrito
sandwich?
I feel your
pain?
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
One-dimension
of straight lines that are closed. Three-dimensions
Here is a list of the most basic polygons:
Triangle
3-sided
Hexagon
6-sided
Quadrilateral 4-sided
Pentagon
5-sided
Heptagon
7-sided
Octagon
8-sided
Polygons are either
This is a
or
.
pentagon because ALL of its
sides and angles are
.
Congruent – having the same measure
Hash marks indicate sides with the same length.
Angle arcs indicate angles of the same measure.
This is an
pentagon because
some of its sides and angles
are not congruent.
Part I
Yep!
I got it on
sale!
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?
I wouldn’t say a
bazillion!
Just a few?
One must
know what one is
getting into before
one gets into it,
Professor!
Why, are we counting?
There are just a few basic ways
that we classify or name
triangles!
Just check
this out!
We classify or name triangles by their angles.
Acute Triangle
All angles < 90°
 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°
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
Classify each triangle by ALL names that apply.
2.
____________________
Acute
1.
____________________
Isosceles
3.
□
____________________
Right
____________________
Isosceles
140°
____________________
Obtuse
____________________
Scalene
So, what do think about classifying
triangles, Mr. Sparkles?
This doesn’t
seem too rough, but
I’ve never seen a cute
triangle?
That’s not what
“acute” actually
means!
It’s nothing
personal. I simply
find triangles fairly
unattractive.
Are they
cute?
I’m not paid enough!
Maybe we should just go take a
look at some quadrilaterals now!
Part II
I know
what you’re thinking…
sweet lid, right?
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?
Have you ever
heard of a square?
Yeah, duh!
Just
checking to
see if you’re
awake!
Well, squares are
quad-ri-lat-er-als!
Let’s classify quadrilaterals from those with the
fewest properties to those with the most properties.
 4-sided polygon
 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.
 Two pairs of parallel sides
 Opposite sides congruent
 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.
 A parallelogram
 4 congruent sides
 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.
WORD BANK
1.
2.
YIELD
trapezoid
equilateral triangle
pentagon
Coffee
rectangle
parallelogram
right triangle
3. parallelogram
octagon
trapezoid
F
square
FA
rhombus
Future Farmers
4.
Work
Zone
of America
5.
6.
World Cup
2014
ITALIA
trapezoid
pentagon
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°.
Match each term with one of the figures.
1. Scalene Obtuse Triangle _____
H
4. Trapezoid _____
A
2. Rhombus _____
G
5. Isosceles Triangle _____
B
6. Equilateral Triangle_____
I
8. Parallelogram _____
C
7. Octagon _____
E
9. Irregular Quadrilateral _____
D
I
A
E
3. Regular Pentagon _____
F
F
B
G
C
D
120°
H
So how do you feel about classifying
two-dimensional figures, Sparky?
I am a
classifying polygaterals
and quadrigonials
beast,It’s
sir!a
promise,
sir!
I’m not sure
you…
Ok! How many sides
does a heptagon have?
I’ll prove
it! Ask me a
question!
That’s easy!
Extinct dinosaurs
don’t have any
sides!
Promise me you’ll
look over the notes!
©Mike’s Math Mall