Geometry lines and angles

point

location, has no size, named by a capital letter

skew lines

non coplaner never parallel do not intersect

parallel planes

planes that do not meet

coplaner

points or lines in the same plane

collinear

points that lie on the same line

opposite rays

rays that are colinear and share a common end point

congruent segments

segments that have the same measure

adjacent angles

share a common ray and vertex

linear pair

two angles that create a straight line

intersecting planes

when 2 planes intersect they meet at exactly one line

intersecting lines

when lines meet at exactly one point

equation of a horizontal line

y=b

complimentary angles

2 angles whose sum is 90 degrees

Zero slope

A horizontal line

What makes 2 lines parallel ?

If they share the same slope

Corresponding angles

The f pattern these angles are congruent

supplementary angles

angles whose sum is 180 degrees

parallel lines

coplaner lines that do not intersect

space

the set of all points

equation of vertical lines

x=b

equation of a line

y= mx+b the m is the slope and b is the y intercept

how to construct an angle bisector

1) place the compass on the vertex of the angle and draw a small arc that intersects both rays 2) using the same compass setting place your compass where the the arc intersects the rays and swing another arc do the same on the other intersection 3)the new arcs should intersect with one another, using a straight edge draw a line from the vertex through the intersection of the arcs

How to do a midpoint construction

1) put the compass on the end of the line and create an arc with your compass opened more than half way. Keep the compass open to the same distance for step two 2)create a second arc and make sure to intersect the first arc with the arc you just made 3)use a straight edge to draw a line through both of the intersections of the arc

how to construct congruent angles

1)draw a ray with an end point 2)with a compass on the point of the original angle draw an arc that intersects both of the rays connected to it 3)with the compass opened to the same distance put it on the endpoint of the ray you drew in step one, draw an arc that intersects the ray 4) open your compass to the distance of the two points made by the arc on the original angle, keep your compass to the same distance and put it on the intersection of the arc and the ray you drew

Transversal

A line that goes through 2 parallel lines

What makes lines perpendicular?

If the 2 lines have negative reciprocals slopes

Slope formula

M = y2 - y1 --------- x2 - x1

Same side interior angles

The inside of the c pattern these angles are supplementary

Alternate interior angles

The inside of the z pattern and the angles are congruent

net

a 2 dimensional pattern that you can fold to create a 3 dimensional figure

plane

a flat surface with no thickness, contains many line, any 3 non collinear points can form a plane

line

a line is a series of points extended in 2 opposite directions with out end

perpendicular bisector

a line that cuts a segment into 2 equal parts at 90 degrees

perpendicular lines

a line that forms a right angle

ray

a part of a line, one end point and extends indefinitely in one direction

midpoint

a point in the middle of a line segment

angle bisector

a ray that divides an angle in to two congruent angles

Undefined slope

Vertical line

congruent angle

angles with the same measure

segment bisector

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

line segment

can be measure, has two end points

distance formula

d= √ (x1-x2)^2 + (y1-y2)^2

angle

formed by two rays with the same endpoint

equation in point slope form

(y-y1))

Negative slope

Starts at the top left corner and ends in the lower right corner

Positive slope

The line starts at the lower left corner and ends at the upper right corner

Same side exterior angles

The outside of the c pattern these angles are supplementary

Alternate exterior angles

The outside of the z pattern these angles are congruent

Slope

The ratio of vertical to horizontal change in a line, also known as the rate of change

Vertical angles

They are opposite angles that share a point these angles are congruent