Geometry Fundamentals (Test 1)

Distance formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

Midpoint formula

(x₁+x₂)/2, (y₁+y₂)/2

Point

A location in space that is represented by a dot and has no dimension. It is named with one capital letter.

Ray

A part of a line that starts at an endpoint and extends forever in one direction. It is named with the endpoint first, then any other point on the ray.

Line

set of infinite points on a straight path extending in two opposite directions. It is named with two capital letters on the line or one script letter.

Plane

a flat surface that has no thickness and extends forever. It is named with three non-collinear points or a script capital letter

Line segment

part of a line with two endpoints and all the points between them. It is named with two endpoints (capital letters) in any order

Collinear

points that lie on the same line

Non-collinear

points that do not lie on the same line

Coplanar

points that lie on the same plane

Non-coplanar

points that do not lie on the same plane

Intersection of two lines

point

intersection of two planes

line

Distance

the absolute value of the difference of the coordinates

Congruent Segments

segments that have the same length

Segment bisector

a segment, ray, line, or plane that intersects a segment at its midpoint

Segment Addition Postulate

If B is between A and C, then AB + BC = AC

Midpoint

A point that divides a segment into two congruent segments

Pythagorean Theorem

a²+b²=c² where a and b represent the legs of a right triangle and c represents the hypotenuse

Horizontal distance

Distance measured only in the horizontal direction. The change in the x-coordinate.

Vertical distance

The change in the y-coordinate or vertical change.

Partitioning Segments

x1 + ratio(change in x)

y1 + ratio(change in y)