all about polygons and quadrilaterals
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All About Polygons and Quadrilaterals. Mackenzie Simonsen. Polygons. Triangle- A plane figure with three straight sides and three angles. A way to remember a triangle is that tri- means three and a tri angle has three sides. - PowerPoint PPT PresentationTRANSCRIPT
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All About Polygons and Quadrilaterals
Mackenzie Simonsen
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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
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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
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Angles
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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
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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
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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
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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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