Unit A Flashcards
Space
Set of all points
Point
It is a location that doesn’t have a size. It’s represented by a small dot and it is named by a capital letter.
Line
It is a series of points that extends in two opposite directions without an end. It is named by any two points on a line or with a single lowercase letter.
Collinear Points
Points that lie on the same line
Plane
It is a flat surface that has no thickness. It contains many lines and extends without end in the direction of all its lines. It is named by at least 3 non - collinear points or a single capital letter.
Coplanar
Points and lines in the same plane
Postulate/Axiom
Accepted statement or fact
Segment
It is a part of a line consisting of 2 endpoints and all points in between them.
Ray
Part of a line consisting of 1 endpoint and all the points of the line on one side of the endpoint.
Opposite Rays
Two collinear rays with the same endpoint. Opposite rays always form a line.
Parallel Lines
Coplanar lines that do not intersect.
Skew Lines
Non-coplanar lines that are not parallel and they do not intersect.
Parallel Planes
Planes that do not intersect
Congruent Segments
Two segments with the same length
Midpoint
- a point that divides a segment into 2 segments.
Angle
Formed by 2 rays with the same endpoint
Congruent Angles
Angles with the same measure
Postulate 1-1
Through any 2 points there is exactly 1 line
Postulate 1-2
If 2 lines intersect, then they intersect in exactly 1 point
Postulate 1-3
If 2 planes intersect, then they intersect in exactly 1 line
Postulate 1-4
Through any 3 collinear points there is exactly 1 plane
Ruler Postulate
The points of a line can be put into 1-1 correspondence with the real numbers so that the distance between any 2 points is the absolute value of the difference of the corresponding numbers.
Segment Addition Postulate
If 3 points A, B, and C are collinear and B is between A and C, then
AB + BC = AC.
Bisect
A line, ray, or other segment through a midpoint.
Perpendicular Lines
2 lines that intersect to form right angles
Angle Bisector
Ray that divides an angle into 2 congruent coplanar angles. Its endpoint is at the angle vertex. Within a ray, a segment with the same endpoint is also an angle bisector. The ray or segment bisects the angle.
Perpendicular Bisector
Line, segment, or ray that is perpendicular to the segment at its midpoint, which bisects the segment into 2 congruent segments.
Compass
Geometric tool used to draw circles and parts of circles called arcs
Construction
Use a straightedge and a compass to draw a geometric figure.
Straightedge
Ruler with no markings on it
Protractor Postulate
Rays can be paired with degrees on protractors
Angle Addition Postulate
m<AOC
Theorem
Statement that must be justified with logical reasoning
Vertical Angle Theorem
Vertical angles are congruent
Congruent Complements Theorem
If 2 angles are complements of the same angle, then they are congruent.
Congruent Supplements Theorem
If 2 angles are supplements of the same angle, then they are congruent.
Theorem 2-4
All right angles are congruent
Theorem 2-5
If 2 angles are congruent and supplementary, then they are right angles
Vertical Angle
2 angles whose sides form opposite rays.
They are non-adjacent angles that are formed by intersecting lines.
Adjacent Angle
2 coplanar angles that have a common vertex, common side, and no common interior points.
Complementary Angle
2 angles that have measures that add up to 90 degrees.
Supplementary Angle
2 angles with a sum of 180 degrees
Linear Pair of Angles
2 angles that are adjacent and supplementary.
Interior Angle
Angles that lie between the 2 lines
Exterior Angles
Angles that lie outside the 2 lines
Alternate Interior Angles
Angles that are on opposite sides of the transversal and are between the 2 lines
Alternate Exterior Angles
Angles that are on opposite sides of the transversal and are outside the 2 lines
Same Side Interior Angles
Angles that lie between the 2 lines and are on the same side of the transversal
Same Side Exterior Angles
Angles that are on the same side of the transversal and lie outside the 2 lines
Corresponding Angles
Angles that are on the same side of the transversal and have corresponding positions
Corresponding Angles Postulate
If a transversal intersects 2 parallel lines, then corresponding angles are congruent.
Alternate Interior Angles Theorem
If a transversal intersects 2 parallel lines, then alternate interior angles are congruent.
Alternate Exterior Angles Theorem
If a transversal intersects 2 parallel lines, then alternate exterior angles are congruent.
Same Side Interior Angles
If a transversal intersects 2 parallel lines, then same side interior angles are supplementary.
Same Side Exterior Angles Theorem
If a transversal intersects 2 parallel lines, then same side exterior angles are supplementary.
Addition Property
If a=b, then a+c=b+c
Subtraction Property
If a=b, then a-c=b-c
Multiplication Property
If a=b, then a times c=b times c
Division Property
If a=b, then a/c=b/c
Reflexive Property
Any geometric figure is congruent to itself. <ABC
Symmetric Property
If one figure is congruent to another figure, then the second figure is congruent to the first. If <ABC.
Transitive Property
If one figure is congruent to the second figure and the second figure is congruent to the third figure, then the first figure is congruent to the third.
