Math 252

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Euclidean Geometry

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Geometric/Measurement

Volume

Volume of a Sphere 4/3(πr³)

Volume of a Cylinder πr² x height

Volume of a Cone ⅓ (πr² x height)

Volume of a Pyramid ⅓(surface area of base x height)

Volume of a Triangular Prism ½(surface area of base x height)

Volume of a Prism Surface area of base x height

Pythagorean Theorem

a² + b² = c² Only works for right triangles Atleast one angle must be 90 degrees If.. a² + b² ≠ c² then it is not a right triangle and pythagorean thereom does not work

Surface Area

Surface area of sphere 4πr² for a hemisphere you must add the face it looks sliced on

Surface area of Cone πr² + πrs

Surface area of pyramid area of base x 2(base x slanted height)

Surface area of Cylinder 2πr² + 2πrh When sliced you must add the surface area of the side it is sliced on

Surface area of Prism 2(base x height) + 2(length x base) + 2(length x height) When doing a triangular prism it is half of the formula

Area and Perimeter

D=6 Pi=3.14 C=18.84u

R=3 Pi=3.14 A=28.26u2

Radius=R

Diameter=D

Pi=3.14

Base1=3 Base2=5 Height=4 1/2(b1+b2)h=16u2

Base=4 Height=5 BH1/2=10u2

Base=2 Height=5 BH=10u2

Length=8 Width=4 LW=32cm2

Geometric Figures

Supplementary: the sum of the measure of two angles is 180 Complimentary angles: the sum of the measures of two complementary angles is 90 degrees Congruent angles: all angles are the same Vertical angles: a pair of angles whose sides are two pairs of opposite rays Corresponding angles: have the same angle measures in degrees Classification of angles: types of angles include acute, obtuse, right and straight angle. Angles can also be adjacent or vertical Angle: a figure formed by two rays

Classifications of Polygons:

Rectangle: a parallelogram with a right angle.

Parallelogram: a quadrilateral in which each pair of opposite sides are parallel.

Isosceles trapezoid: a trapezoid with congruent base angles.

Trapezoid: a quadrilateral with at least one pair of parallel sides.

Kitequadrilateral with two adjacent sides congruent and the other two sides are also congruent.

Isosceles triangle: a triangle with at least two congruent sides.

Scalene triangle: triangle with no congruent sides

Obtuse triangle: a triangle containing one obtuse angle

Acute triangle: a triangle in which all the angles are acute

Right triangle: a triangle in which all the angles are acute.

Polygon: all sides are congruent and all angles are congruent

Prisms: a prism is a polyhedron in which two congruent faces "the bases" lie in parallel planes and the other faces (lateral faces) are bounded by parallelograms

Cones: The union of the line segments connecting a point P with each point of a simple, closed curve, the simple, closed curve in the interior of the group

Cylinders: A simple closed surface that is not a polyhedron

Right Pyramids:

Triangular Pyramid

Square Pyramid

Hexagonal oblique prism

Triangular Right Prism

Quadrilateral Right Prism

Hexagonal Right Prism