Polygons and Angles

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ASVAB

Algebra

Quadrilateral and Polygons

Angles

Last updated 1:30 AM on 10/30/22
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26 Terms

1
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Equilateral triangles
________ has 3 equal sidesAll three angles are=
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Quad
Type
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a quadrilateral with 1 pair of parallel sides.Bases
2 parallel sides of a trapezoid
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The formula of the area=1/2 (sum of the lengths of the base)(height)Example
1/2 (a+b)(h)=area
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Interior Angles
add up to 180 degrees
X +50+100=180
add up to 180 degrees X +50+100=180
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Exterior Angles
= to the sum of the two interior angles that are not adjacent to that exterior angle
y= angle 1 + angle 2
= to the sum of the two interior angles that are not adjacent to that exterior angle y= angle 1 + angle 2
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Easy Peasy Perimeter
Any Polygon = add all sides
6+8+4=18cm
Any Polygon = add all sides 6+8+4=18cm
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Area of a Triangle
The height is the perpendicular distance between the sides that’s chosen as the base and the opposite vertex.
Area of triangle=1/2 (base) (height)
The height is the perpendicular distance between the sides that’s chosen as the base and the opposite vertex. Area of triangle=1/2 (base) (height)
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Similar Triangles
have the same shape, although different shapes.
Corresponding angles are =Corresponding sides are proportional
a/p=b/q=d/r
Angle equivalents
have the same shape, although different shapes. Corresponding angles are =Corresponding sides are proportional a/p=b/q=d/r Angle equivalents
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Isosceles
has 2 equal sides
Angles opposite from the equal sides, are called base angles.
If AB=AC Then,
<ABC=<ACB
has 2 equal sides Angles opposite from the equal sides, are called base angles. If AB=AC Then, <ABC=<ACB
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Equilateral triangles
has 3 equal sides All three angles are =
All angles in a equilateral triangle measure 60 degrees, regardless of length of sides.
has 3 equal sides All three angles are = All angles in a equilateral triangle measure 60 degrees, regardless of length of sides.
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Right Triangle
Every right Triangle has has exactly 2 acute triangles
Legs- are sides opposite to the acute angle
Hypotenuse- side opposite to right angle
Every right Triangle has has exactly 2 acute triangles Legs- are sides opposite to the acute angle Hypotenuse- side opposite to right angle
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Pythagorean Theorem
a^2 + b^2=c^2
a^2 + b^2=c^2
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Quadrilateral basics
Add all sides for perimeter a+b+c+d=perimeter
Add all sides for perimeter a+b+c+d=perimeter
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Parallelogram
Two sets of parallel sides
Opposite sides are equal
Opposite angles are equal
Adjacent angles add up to180 degrees
Area= (base)(height)
Two sets of parallel sides Opposite sides are equal Opposite angles are equal Adjacent angles add up to180 degrees Area= (base)(height)
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Rectangle
A parallelogram w/ 4 right angles
Opposite sides are equal
Area= (length) (width)
Perimeter= 2(l+w)
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Rhombus
Has 4 =sides
Opposite sides are parallel to one another
Perimeter=4s
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Square
4 =sides
Area= (side)^2
P=4s
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Trapezoid
Quadrilateral with 1 pair of parallel sides.
Bases- 2 parallel sides of a trapezoid
Area=1/2 (sum of the lengths of the base)(height)
Example: 1/2(a+b)
Quadrilateral with 1 pair of parallel sides. Bases- 2 parallel sides of a trapezoid Area=1/2 (sum of the lengths of the base)(height) Example: 1/2(a+b)
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Circumference
= 2(pie*r)=(pie*d)
= 2(pie*r)=(pie*d)
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Area of a circle
= Pie*r^2
= Pie*r^2
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Volume of a rectangular solid box (3D)
= lwh
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Surface area of box
= 2lw+2wh+2lh
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Volume of a cylinder (3D)
= pie*r^2*h
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To find the surface area of any 3 dimensional figure
add the areas of each side of the figure.
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Formula for surface area of a cylinder is
SA= 2(pie*r^2)+2(pie)
finding the surface area of a cylinder involves adding the area of both of the circular ends to the area of the curved side. Note that, if the sides of a cylinder were “unrolled”, they’d form a rectangle.