Geom Ch.1 terms and formulas

Point

Names a location, has no dimension, is a small dot, represented by a capital letter

Line

Is made up of points with no thickness or width, one line through two points, has arrows, named by two capital letters or two cursive letters

Collinear

Points on the same line are…

Plane

A flat surface made up of points that extend infinitely in all directions, has no thickness, there is 1 of these through 3 noncollinear points, drawn as a parallelogram, has no boundaries, named by a capital cursive letter or 3 noncollinear points

Segment

The part of a line that consists of two endpoints and all the points between them

Ray

The part of a line that starts at an endpoint and extends infinitely in 1 direction

Intersection

Two or more geometric figures in the set of points they have in common \[two lines intersect at a point, lines can intersect planes, plane can intersect each other\]

Postulate

A statement that doesn’t need proof to be accepted as true

Postulate 1-1-1

Through any two points there is exactly 1 line

Postulate 1-1-2

Through any 3 noncollinear points there is exactly 1 plane

Postulate 1-1-3

If 2 points lie in a plane, then the line containing these points lies in a plane

Postulate 1-1-4

If two lines intersect, then they intersect at exactly 1 point

Postulate 1-1-5

If two planes intersect, then they intersect at exactly 1 line

Distance

The absolute value of the difference of the coordinate of two points

Congruent segments

Segments with the same length

Construction

Methods of creating geometric figures using a ruler, protractor, or compass

Midpoint

The point which bisects a line into two equal parts

Segment bisector

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

Angle

Formed by two rays or sides that have a common endpoint called a vertex

Right angle

An angle that measures to exactly 90 degrees

Acute angle

An angle that measures below 90 degrees

Obtuse angle

An angle that measure over 90 degrees

Straight angle

An angle that measures at exactly 180 degrees

Reflex angle

(Not on the test, but good to know) An angle that measures over 180 degrees

Congruent angles

Angles with the same measure

Angle bisector

A ray that divides an angle into two congruent halves

Angle Addition Postulate

If D is in the interior of

Adjacent angles

Two angles that lie in the same plane and have a common vertex and a common side, but have no common interior points

Linear pair

A pair of adjacent angles with noncommon sides that are opposite rays

Vertical angles

Two nonadjacent angles formed by two intersecting lines

Complementary angles

Two angles with measures that add up to 90 degrees

Supplementary angles

Two angles with measures that add up to 180 degrees

Coordinate plane

A plane that is divided into four regions by a horizontal line (x-axis) and a vertical line (y-axis). The location…of a point given is by an ordered pair (x,y)

Pythagorean theorem

a²+b²=c²

Distance formula

√(x₂-x₁)²+(y₂-y₁)²

Midpoint on a coordinate plane formula

x₁+x₂/2, y₁+y₂/2