Carmon Geometry Unit 1A

vertical angles

two nonadjacent angles formed by two intersecting lines

supplementary angles

Two angles whose sum is 180 degrees

linear pair

a pair of adjacent angles whose noncommon sides form a straight angle

complementary angles

Two angles whose sum is 90 degrees

adjacent angles

two angles that share a common vertex and side, but have no common interior points

angle bisector

a ray that divides an angle into two congruent angles

Angle Addition Postulate

If B is in the interior of

acute angle

an angle that measures less than 90 degrees

right angle

an angle that measures 90 degrees

obtuse angle

An angle that measures between 90 and 180 degrees

straight angle

an angle that measures 180 degrees

Distance Formula

finds the length of a segment; on the reference sheet

midpoint formula

finds the point in the middle of two other points; answer will be a POINT (x, y)

Midpoint

A point that divides a segment into TWO EQUAL PARTS

segment bisector

a segment, ray, line, or plane that intersects a segment at its midpoint; means there are TWO EQUAL PARTS

Collinear

points that lie on the same line

Coplanar

points, lines, segments, and/or rays that lie in the same plane

point

an exact location in space

Line

A set of connected points continuing without end in both directions.

ray

A part of a line, with one endpoint, that continues forever in one direction

segment

A part of a line consisting of two endpoints and all points between them.

plane

A two-dimensional flat surface that extends forever in all directions

endpoint

a point at the end of a segment or ray; the segment or ray does not go past this point.

Two planes intersect at a _________________

line

Two lines intersect at a _____________

point

intersection

A point or set of points where lines, segments, rays, or planes cross each other.

Segment Addition Postulate

If B is between A and C, then AB + BC = AC. little part + little part = BIG part

congruent segments

segments that have the same length, marked in a figure with "slashies"

congruent angles

angles that have the same measure, marked in a figure with arcs

postulate

a math rule, sort of common sense

opposite rays

two rays that have a common endpoint and form a line

How do you name a LINE?

two points in any order and the line symbol <-> above it or write out "line" with a lowercase letter; line "s" in cursive

How do you name a SEGMENT?

Two endpoints with capital letters and "—" above it

How do you name a RAY?

Write the endpoint first and then another point on the ray. Use the ray symbol: ->

How do you name a PLANE?

A (script) capital letter OR three points (or more) that aren't on one line

How do you name an ANGLE?

With the word "Angle" or the angle symbol and the three points (vertex in middle)

Ex: Angle ABC, Angle CBA, ∠ABC, ∠CBA,

Also with the vertex Ex. ∠B, (if there is only one angle)

or with a number Ex. Angle 1 or ∠1

"line XY"

means the line goes through X and Y and continues forever in both directions

"ray AB"

means the ray starts at A and goes through B continuing forever in that one direction.

"segment CD"

just the part of the line between C and D; does not continue past either point