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