D prisms(234)

A three dimensional figure has a length, width, and height. These figures are often called prisms. A rectangular prism is a rectangle with a height. A cube is a square with all equal dimensions (etc.). The area of a prism is called its volume, or capacity it can hold. The volume is calculated by multiplying all three dimensions together . Each prism has a faces, vertices, and edges. A face is the amount of shapes that make up the prism. Edges are how many lines a prism has. Vertices(single vertex) are the conjoined lines that form angles of the faces of a prism. Every figure has some of these features, except for a sphere with a single face.

Here is an example:

Trickometry(235)

That cube above has a volume of 216 cubic inches. When you find volume, the answer has to be cubed because its 3 dimensional. Let’s apply this cube as an empty box. Let’s say you want to fill this box with bricks. The heights of the bricks are 2 inches, the length being 2 inches, and the width being 3 inches. How many bricks can you fit in this box? The volume of each brick is 12 inches cubed. You just divide 216 by 12, and you get 18 bricks.

Cylinders and cones(236)

A cylinder and cone both have a circle in them. A cone has one and a cylinder has 2 on each end. The formula for calculating volume of a cylinder is .

Here is an example:

Geometric Proofs

Everything having to do with geometry has to be proven the concept is correct. A geometric proof proves a theory that says that what is stated is true referring to postulates and definitions leading to prove a theorem. Other theorems can be used that have already been proved.

Geo Post 1

The points on a line can be paired with real numbers in a such a way that any 2 points can have the coordinates 0 and 1. Once a coordinated system has been chosen in this way, the distance between any 2 points equals the absolute value of the difference of the coordinates.

Geo Post 2

Known as the segment addition postulate that adds two rays within a whole segment to equal that segment.

Geo Post 3

Known as the protractor postulate

Geo Post 4

Known as the angle addition postulate that adds 2 angles to be equivalent to the angle that is within both those angles.

Geo Post 5

A line contains at least 2 points; a plane contains at least 3 points not all in one line; space contains at least 4 points not all in one plane.

Geo Post 6

Through any two points, there is exactly one line

Geo Post 7

Through any 3 points, there is at least one plane, and through any non collinear points there is exactly one plane

Geo Post 8

If 2 points are in a plane, then the line that contains those points is in a plane

Geo Post 9

If 2 planes intersect, then the intersection is a line

Geo Post 10

If 2 parallel lines are cut by a transversal, the corresponding angles are congruent

Geo Post 11

(Converse of postulate 10)

Geo Post 12

Known as the SSS postulate, if 3 sides of one triangle are congruent in the 3 sides of another triangle, the triangles are congruent.

Geo Post 13

Known as the SAS postulate, if 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, the triangles are congruent.

Geo Post 14

Known as the ASA postulate, if 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another, the triangles are congruent.

Geo Post 15

Known as the AA similarity postulate, if 2 angles of 1 triangle are congruent to 2 angles of another, the triangles are similar

Geo Post 16

Known as the arc addition postulate, the measure of the arc formed by 2 adjacent arcs is the sum of the measure of these 2 arcs.

Geo Post 17

Known as the square(d) postulate, the area of a square is the square of the length of a side.

Geo Post 18

Known as the area congruence postulate, if two figures are congruent, they have the same area.

Geo Post 19

Known as the area addition postulate, the area of a region is the sum of the areas of its non-overlapping parts.

Theorem 1-1

If 2 lines intersect, then they intersect at exactly one point:

Given: B is the midpoint of AC and DE

Дата добавления: 2015-11-16