Download All About Polygons and Quadrilaterals

All About Polygons and Quadrilaterals
Mackenzie Simonsen
Polygons
1
• Triangle- A plane figure with three straight sides and three angles.
A way to remember a triangle is that tri- means three and a triangle
has three sides.
• Quadrilateral- A plane figure with 4 straight sides and 4 angles. A
way to remember is that quad- means 4.
• Pentagon- A plane figure with 5 straight side and 5 angles. A way to
remember is the Pentagon in Washington D.C., it have five sides.
• Hexagon- A plane figure with 6 straight sides and 6 angles. A way to
remember is know that hex- means six.
• Heptagon- A plane figure with 7 straight sides and 7 angles. To
remember heptagon you only have to know all the others. Like
process of elimination.
• Octagon- A plane figure with 8 straight sides and 8 angles. To
remember and octagon just think of a stop sign, they are all
octagons.
• Nonagon- A plane figure with 9 straight sides and 9 angles.
Nonagon is the only –gon that starts with the letter n, nine is the
only singe digit number that starts with the letter n.
• Decagon- A plane figure with 10 straight sides and 10 angles. When
counting to ten in Spanish, 10 starts with a d and so does decagon.
Angles of Polygons
Interior
•
To find the sum of the interior angle take
the number of sides on the polygon the
subtract two from that number and
multiply by 180º.
Find the sum of the interior angles of an
octagon. Use the equation (n-2)180.
(8-2)180= 6*180= 1080º in an octagon.
• To find one interior angle take the final
number from the first step and divide it by
the number of sides
Find the measure of one interior angle of
an octagon. (8-2)180= 6*180= 1080º / 8=
135º in one interior angle of an octagon.
2
Exterior
• All exterior angles add up to
360º.
The answer is always 360º.
• Find one angle by dividing 360º
by the number of sides.
Find the measure of one exterior
angle of an octagon.
360º/ 8= 45º
How to Find the Number of Sides
• When given the sum of the interior angle
measure use the equation: (n-2)180
• EXAMPLE: The sum of the interior angles of an ngon are 2,340º, how many sides are in this
polygon?
• There are 15 sides in this polygon
(n - 2)180 = 2340
180
n - 2 = 13
n = 15
Parallelograms
Properties
• Both sets of opposites sides
are congruent and parallel
• Corresponding angles add
up to 180º
• Opposite angles are
congruent
• Diagonals bisect each other
and the parallelogram
• It is a quadrilateral.
3
Picture
Angles
3
Angles
3
Diagonals
3
Properties
• 4 right angles
• Opposite sides are
congruent
• Diagonals are congruent
4
Picture
• Find the measure of the
missing angle
• m<1= 90º
4
• Find the value of x.
• X= 30
• Find the length of side
DB.
4
Rhombus
Properties
• Diagonals are
perpendicular
• All sides are congruent
• Diagonals bisect angles
making them congruent
5
• ANGLES
• Find the measure of
angle one
• M<1= 90º
Rhombus
• ANGLES
• Find the measure of
angle 2
• m<2= 25º
5
• DIAGONALS
• Find the length of LN
• 4x-1=3x+2
• X=3
• LN= 22
1. 4 right angles
2. All sides are congruent
3. Is both a rhombus and a rectangle
6
Trapezoids
Regular
• One set of parallel lines
• Midsegment is equal to
1/2(top base x bottom base)
• Midsegment is parallel to
the bases
7
Isosceles
• One set of parallel lines
• Legs are congruent
• Base angles are congruent
• Diagonals are congruent
Trapezoid/ Isosceles Trapezoid
x
y
z
y= 1
7
x · z)
(
2
Trapezoids
Angles
• Find the measure of angle 1
and 2
• 180º - 56º= 124º
• M<1= 124º
• M<2=56º
Angles
• Find the measure of angles
1 and 2
• M<1= 23º
• M<2= 157º
• 180º - 157º = 23º
1
56º
7
2
2
1
157º
• Find x and the measure of side EF
180
13
A
4x- 15
B
4x -15 + 5x -10 )
2(
4x = 4x -15 + 5x -10
2x = 1
4x = 9x - 25
E
2x
25 = 5x
F
x=5
2·5 =10
5x-10
D
7
EF= 10
C
Median