Unit 1 Flashcards
Point
A point indicates a location and has no size. Represented a by a dot and a capital letter, such as A .
Line
A straight path that extends in two opposite directions without end and has no thickness. A line contains infinitely many points. Named by any two points on the line, such as AB (read “line AB ”) or BA, or by a single lowercase letter, such as line / .
Plane
A flat surface that extends without end and has no thickness. A plane contains infinitely many lines.You can name a plane by a capital letter, such as plane P, or by at least three points in the plane that do not all lie on the same line, such as plane ABC.
Coplanar
Points that lie on the same plane, all points of any line are coplanar.
Collinear
Points that lie on the same line
Geometric Figure
Set of points
Space
The set of all points in three dimensions.
Segment
Part of a line that consists of two endpoints and all points between them. name a segment by its two endpoints, such as AB (read “segment AB ”) or BA
Ray
Part of a line that consists of one endpoint and all the points of the line on one side of the endpoint. You can name a ray by its endpoint and another point on the ray, such as AB > (read “ray AB ”). The order of points indicates the ray’s direction.
Opposite Rays
Two rays that share the same endpoint and form a line. Name opposite rays by their shared endpoint and any other point on each ray, such as CA > and CB > .
Postulate/Axiom
An accepted statement of fact used to justify answers in proofs
Postulate 1-1
Through any 2 points there is exactly one line that passes both of them
Postulate 1-2
If two distinct lines intersect, then they intersect in exactly one point.
Postulate 1-3
If two distinct planes intersect, then they intersect in exactly one line.
Postulate 1-4
Through any three noncollinear points there is exactly one plane.
Ruler Postulate/ 1-5
Every point on a line can be paired with a real number. This makes a one-to-one correspondence between the points on the line and the real numbers. The real number that corresponds to a point is called the coordinate of the point.
Segment Addition Postulate
If three points A , B , and C are collinear and B is between A and C , then AB + BC = AC
Equal sign vs. Congruent Sign
Equal sign is used for the measure of things, whereas congruent is used for comparing the shape or figure itself
Angle
A figure formed with 2 rays and an endpoint, the rays are the “sides” and the endpoint is the “vertex”
Interior of an Angle
The region containing all of the points between the two sides of the angle.
Exterior of an Angle
The region containing all of the points outside of the angle.
Protractor Postulate
Consider OB > and a point A on one side of OB > . Every ray of the form OA > can be paired one to one with a real number from 0 to 180.
Acute Angle
A measure less than 90
Right Angle
A 90 degree measure
Obtuse Angle
A measure more than 90 degrees
Straight Angle
A measure of 180 degrees
Congruent Angles
Angles with the same measure
Postulate 1-8/Angle Addition Postulate
If point B is in the interior of ∠AOC , then m ∠AOB + m ∠BOC = m ∠AOC
The 2 inside angles in a big angle add up to make the big angle.
Adjacent Angles
Two coplanar angles with a common side, a common vertex, and no common interior points.
Vertical angles
Two angles whose sides are opposite rays.
Complementary angles
Two angles whose measures have a sum of 90. Each angle is called the complement of the other.
Supplementary angles
Two angles whose measures have a sum of 180. Each angle is called the supplement of the other.
Unmarked Diagram Conclusions
- Angles are adjacent.
- Angles are adjacent and supplementary.
- Angles are vertical angles.
Unmarked Diagram Conclusions that can’t be made
*Angles or segments are congruent.
*An angle is a right angle
*Angles are complementary.
Linear Pair Postulate/1-9
If two angles form a linear pair, then they are supplementary.
Linear Pair
A pair of adjacent angles whose noncommon sides are opposite rays. The angles of a linear pair form a straight angle.
Straightedge
A ruler with no markings on it
Compass
A geometric tool used to draw circles and parts of circles called arcs
Construction
A geometric figure drawn using a straightedge and a compass.
Perpendicular Lines
Two lines that intersect to form a right angle
Perpendicular bisector
A segment is a line, segment, or ray that is perpendicular to the segment at its midpoint.
Midpoint on a number line
The coordinate of the midpoint M of AB is (a + b)/2
Midpoint in the coordinate plane
Given AB where A ( x 1 , y 1 ) and B ( x 2 , y 2 ) , the coordinates of the midpoint of AB are M ( x 1 + x 2)/2 , (y 1 + y 2)/2.
Distance Formula
d = The square root of
( x 2 -x 1 ) squared + ( y 2 -y 1) squared
