What is a Polygon????
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Transcript What is a Polygon????
Polygons
Brought to you by Cavis for President
What is a Polygon????
Any ideas?
Write down what you think it is for #1.
A polygon is a closed plane figure with 3 or more sides (all
straight lines, no curves).
Classifying Polygons by # of Sides
3 sided Polygon = Triangle
Hint: Think “Tri”cycle,
“tri”pod, “Tri”lateration
(Tri means 3)
Classifying Polygons by # of Sides
4 sided Polygon = Quadrilateral
Hint: Think “Quad”rant,
“Quad”ruple, “Quad”
(AKA 4-Wheeler)
Classifying Polygons by # of Sides
5 sided Polygon = Pentagon
Hint: Think “Pent”athalon,
or the government building
“The Pentagon”
Classifying Polygons by # of Sides
6 sided Polygon = Hexagon
Hint: Both “Hexagon” and
“Six” have an ‘x’ in them
Classifying Polygons by # of Sides
7 sided Polygon = Heptagon
Hint: ???
Classifying Polygons by # of Sides
8 sided Polygon = Octagon
Hint: “oct”opus – 8 legs
Classifying Polygons by # of Sides
9 sided Polygon = Nonagon
Hint: “Non” is similar to
“Nine”
Classifying Polygons by # of Sides
10 sided Polygon = Decagon
Hint: Think “Dec”ade (10
years
Classifying Polygons by # of Sides
11 sided Polygon = Hendecagon
Hint: ???
Classifying Polygons by # of Sides
12 sided Polygon = Dodecagon
Hint: ???
Classifying Polygons by # of Sides
Q: What do we call a polygon with more than 12 sides?
A: An ‘n’-gon where ‘n’ is the number of sides
Ex: a 20 sided polygon is a 20-gon
6.2 Properties of Parallelograms
• A parallelogram is a quadrilateral with both pairs of
opposite sides parallel.
• In a quadrilateral, opposite sides do not share a
vertex and opposite angles do not share a side.
Theorem 6.3
• If a quadrilateral is a parallelogram, then its opposite
sides are congruent.
Consecutive Angles
• Angles of a polygon that share a side are consecutive
angles.
Theorem 6.4
• If a quadrilateral is a parallelogram, then its
consecutive angles are supplementary.
Using Consecutive Angles
•
A.
B.
C.
D.
What is the measure of angle P in parallelogram PQRS?
26°
64°
116°
126°
mP mS 180
mP 64 180
mP 116
Theorem 6.5
• If a quadrilateral is a parallelogram, then its opposite
angles are congruent.
Theorem 6.6
• If a quadrilateral is a parallelogram, then its diagonals
bisect each other.
Using Algebra to Find Lengths
• Solve a system of linear equations to find the values
of x and y in parallelogram KLMN. What are KM
and LN?
Using Algebra to Find Lengths
KP MP
LP NP
y 10 2 x 8
x y2
y 10 2( y 2) 8
y 10 2 y 4 8
10 y 4
14 y
x 14 2
x 16
KM 2( KP)
KM 2( y 10)
2(14 10)
48
LN 2( LP)
LN 2x
2(16)
32
Theorem 6.7
• If three (or more) parallel lines cut off congruent
segments on one transversal, then they cut off
congruent segments on every transversal.
Classifying Polygons by # of Sides
# of Sides
Name
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
11
Hendecagon
12
Dodecagon
Two Types of Polygons
Convex – all vertices point outward
Concave – at least one vertex points
inward towards the center of the polygon
(The side looks like it “caved” in)
Regular Polygons
A Regular Polygon is a polygon in which all sides are the same
length.
Equilateral
Triangle
Square
Review of Similar Triangles
• 2 Triangles are similar if they have the same
shape (i.e. the same angle in the same positions)
Similar Polygons
The same is true of polygons. 2 polygons are
similar if they have the same angles in the same
positions (i.e. same shape)
Similar
Trapezoids
^ Similar Pentagons ^
Similar
Rectangles
60 120
120
6
6
50°
130°
Essential Question
• What are properties of sides and angles
of rhombuses, rectangles, and squares?
Properties of Special Parallelograms
• In this lesson, you will study three special
types of parallelograms: rhombuses,
rectangles and squares.
A rhombus is a parallelogram
with four congruent sides
A rectangle is a
parallelogram with four right
angles.
A square is a parallelogram
with four congruent sides and
four right angles.
Venn Diagram shows relationships-- MEMORIZE
• Each shape has the properties of every group that it
belongs to. For instance, a square is a rectangle, a
rhombus and a parallelogram; so it has all of the
properties of those shapes.
parallelograms
rhombuses
rectangles
squares
Rhombuses
Rectangles
Some examples of a rhombus
Examples of rectangles
Examples of squares
Ex. 1: Describing a special parallelogram
•
a.
b.
Decide whether the statement is always, sometimes, or never true.
A rhombus is a rectangle.
A parallelogram is a rectangle.
parallelograms
rhombuses
rectangles
squares
Rhombuses
Rectangles
Ex. 1: Describing a special parallelogram
Decide whether the statement is always, sometimes, or never true.
b.
A parallelogram is a rectangle.
c.
The statement is sometimes true. Some parallelograms are rectangles. In the
Venn diagram, you can see that some of the shapes in the parallelogram box
are in the area for rectangles, but many aren’t.
parallelogra
ms
rhombuses
rectangles
squares
Rhombuses
Rectangles
Family of Parallelograms
• Types of Parallelograms
Foldable
1. Take out a piece
of notebook paper
and make a hot
dog fold over from
the right side over
to the pink line.
Foldable
2. Now, divide the right
hand section into 5
sections by drawing 4
evenly spaced lines.
3. Use scissors to cut
along your drawn line,
but ONLY to the crease!
The fold crease
Foldable
4. Write
QUADRILATERALS
down the left hand
side
The fold
crease
Foldable
5. Fold over the top
cut section and write
PARALLELOGRAM
on the outside.
6. Reopen the fold.
The fold
crease
Foldable
7. On the left hand
section, draw a
parallelogram.
8. On the right hand
side, list all of the
properties of a
parallelogram.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel
Foldable
* Fold over the
second cut section
and write
RECTANGLE on the
outside.
* Reopen the fold.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel
Foldable
* On the left hand
section, draw a
rectangle.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel
1. Special parallelogram.
* On the right hand
side, list all of the
properties of a
rectangle.
2. Has 4 right angles
3. Diagonals are congruent.
Foldable
* Fold over the third
cut section and write
RHOMBUS on the
outside.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel
1. Special parallelogram.
2. Has 4 right angles
3. Diagonals are congruent.
* Reopen the fold.
Foldable
* On the left hand
section, draw a
rhombus.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel
1. Special parallelogram.
* On the right hand
side, list all of the
properties of a
rhombus.
2. Has 4 right angles
3. Diagonals are congruent.
1. Special Parallelogram
2. Has 4 Congruent sides
3. Diagonals are perpendicular.
4. Diagonals bisect opposite angles
Foldable
* Fold over the third
cut section and write
SQUARE on the
outside.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel
1. Special parallelogram.
2. Has 4 right angles
3. Diagonals are congruent.
* Reopen the fold.
1. Special Parallelogram
2. Has 4 Congruent sides
3. Diagonals are perpendicular.
4. Diagonals bisect opposite angles
Foldable
* On the left hand
section, draw a
square.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel
1. Special parallelogram.
* On the right hand
side, list all of the
properties of a
square.
* Place in your
notebook and save
for tomorrow.
2. Has 4 right angles
3. Diagonals are congruent.
1. Special Parallelogram
2. Has 4 Congruent sides
3. Diagonals are perpendicular.
4. Diagonals bisect opposite angles
1. All the properties of parallelogram,
rectangle, and rhombus
2. 4 congruent sides and 4 right
angles
Foldable
* On the left hand
section, draw a
square.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel
1. Special parallelogram.
* On the right hand
side, list all of the
properties of a
square.
2. Has 4 right angles
3. Diagonals are congruent.
1. Special Parallelogram
2. Has 4 Congruent sides
3. Diagonals are perpendicular.
4. Diagonals bisect opposite angles
1. All the properties of parallelogram,
rectangle, and rhombus
2. 4 congruent sides and 4 right
angles
Foldable
* On the left hand
section, draw a kite.
1. Opposite angles are congruent.
2. Consecutive angles are
supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Opposite sides are parallel
1. Special parallelogram.
* On the right hand
side, list all of the
properties of a kite.
2. Has 4 right angles
3. Diagonals are congruent.
1. Special Parallelogram
2. Has 4 Congruent sides
3. Diagonals are perpendicular.
4. Diagonals bisect opposite angles
* Place in your
notebook and save
for tomorrow.
1. All
the properties of
parallelogram, rectangle,
and rhombus
2. 4 congruent sides and 4
right angles
1. The
diagonals of a kite meet
at a right angle.
(2) Kites have exactly one pair
of opposite angles that are
congruent.