All About Polygons and Quadrilaterals

Mackenzie Simonsen

Poly

gons

• 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.

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Angles of PolygonsInterior

• 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.

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

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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 n-gon are 2,340º, how many sides are in this polygon?

• There are 15 sides in this polygon

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.

Picture

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Angles

3

Angles

3

Diagonals

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RECTANGLES

Properties• 4 right angles• Opposite sides are

congruent• Diagonals are congruent

Picture

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Angles of a Rectangle • Find the measure of the

missing angle• m<1= 90º

• Find the value of x.• X= 30

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D i a g o n a l s o f a R e c t a n g l e

• Find the length of side DB.

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RhombusProperties• Diagonals are

perpendicular• All sides are congruent• Diagonals bisect angles

making them congruent

• ANGLES• Find the measure of

angle one• M<1= 90º

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Rhombus

• ANGLES• Find the measure of

angle 2• m<2= 25º

• DIAGONALS• Find the length of LN

• 4x-1=3x+2• X=3• LN= 22

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Squares1.4 right angles2.All sides are congruent3.Is both a rhombus and a

rectangle6

Trapezoids

Regular • One set of parallel lines• Midsegment is equal to 1/2(top base x bottom base)• Midsegment is parallel to

the bases

Isosceles• One set of parallel lines• Legs are congruent• Base angles are congruent• Diagonals are congruent

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Trapezoid/ Isosceles Trapezoid

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x

y

z

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

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1

56º 2

2

1

157º

Median

• Find x and the measure of side EF

4x- 15

2x

5x-10

A B

CD

E F

EF= 10

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