Geometry Terms Flashcards
What makes up a line?
Any two points.
What makes up a plane?
3 noncollinear points
How many lines can be found in 2 points?
Exactly one.
If two lines intersect, exactly where do they do so?
At exactly one point
If two planes intersect, where do they do so?
One line.
Two lines that have a point in common are what kinds of lines?
Intersecting
What are the defining traits of parallel lines?
They are Coplanar (will point in the same direction, otherwise they would intersect) and will never touch
What are the defining traits of skew lines?
They are noncoplanar, allowing the lines to be in different directions. Though they lie on different planes, they will never intersect
What is the intersection of two planes?
A line (always(
Two lines perpendicular to the same plane will be…
Coplanar
Through a given point, how many planes can be perpendicular to a certain line? (Vice versa)
One
If a line is perpendicular to both (2) intersecting lines at their point of intersection, what type of line is it?
The line is perpendicular to the plane determined by the two original intersecting lines
What is the only way two planes can be perpendicular to each other?
One plane must contain the line perpendicular to the second one.
If a line is perpendicular to each of two intersecting lines at their point of intersection, what is the relationship of that line & the plane?
The line is perpendicular to the plane
How can planes be perpendicular to each other?
One plane contains a line perpendicular to the second plane
If a line is perpendicular to a plane, where are lines perpendicular at its point of intersection to that particular line located?
They are located in the same plane
If a line is perpendicular to a plane, what is the relationship between that particular plane and any other plane containing the line itself?
The planes containing the perpendicular line become perpendicular themselves to that specific plane
If a plane intersections two parallel planes, what is the intersection?
Two parallel lines
What shape will two planes form when they intersect at a particular line?
“X”
Perpendicular
Intersection at the 90 degree angle of a line
Parallel
-coplanar
-will never intersect (go in same direction- otherwise would immediately intersect on the same plane)
Skew
Noncoplanar, will never touch (can be in different directions
What is a ray that divides an angle unto 2 equal angles each gave a measure half of the given angle
Angle bisector
What is the angle addition postulate?
In a situation in which D is the interior point in angle
What is the segment addition postulate?
If 3 points are collinear (ex. A, B, C) and there is a point in the middle (B), Then AB + BC = AC
If a point divides a segment unto 2 parts, what is its term given?
Midpoint
Two angles whose sides are opposite rays of each other
Vertical angle
Two coplanar angles with a common vertex (intersecting line) and common side but no common interior points (space inside the angle)
Adjacent angle
Two angles whose measures = 90 degrees
Complementary
Two angles whose measures = 180 degrees
Supplementary
Midpoint formula
M = ( x1 + x2 /2 , y1 + y2/2)
Formula for distance
D = square root of (x2-x1) squared + (y2-y1) squared
Segment adddition postulate
AB + BC = AC
Angle addition postulate
If D is the interior of < ABC, then
What us an angle bisector
A ray dividing an angle into two equal angles which both measure half the given angle in its entirety
Constructing congruent segments
Draw ray longer than given segment (draw abc label one endpoint. Open compass to measure length of original line and draw an arc on second line and label it where the arc and line intersect
Constructing congruent angles
Draw ray and label endpoint, draw an arc that intersects both sides of the angle on the original and label the intersection- copy this on drawn ray. Then measure length of those two points together (height?) And copy it onto your drawn ray. Where they intersect is where you add a line and label
Constructing angle bisectors
Draw arc on original angle and label intersections, draw extended arcs from each individual point and where they intersect is where you connect the dots and draw the line bisecting the angle
Constructing perpendicular bisectors
Open compass to over 1/2 the length of line and draw wide arc on both sides, label and connect where the lines intersect
Constructing perpendicular lines through a point
Start compass at point and draw horizontal arc passing through line twice, label the intersections and make a perpendicular bisector
Constructing equilateral triangles
Copy and label line segment, and without changing compass draw an 2 arcs above line and label their intersection, forming a triangle
