Studied by 14 people
Looks like no one added any tags here yet for you.
Point
is a location in space represented by a dot with no dimension, named with a capital letter.
Line
is a one-dimensional object with no width, extending infinitely in both directions, named by a lowercase letter or two points on it.
Plane
is a flat, two-dimensional surface extending infinitely, with no thickness, named by a capital script letter or three non-collinear points.
Postulates
Statements accepted as true without proof.
Theorems
Statements proven true using undefined terms, definitions, postulates, and other theorems.
Supplementary Angles
Two angles with a sum of 180Ā°.
Complementary Angles
Two angles with a sum of 90Ā°.
Adjacent Angles
Two angles sharing a vertex and side but no interior points.
Linear Pair of Angles
Adjacent angles with non-common sides forming a straight line, summing to 180Ā°.
Vertical Angles
Pair of congruent angles opposite each other formed by intersecting lines.
Types of Triangles
Right, Acute, Obtuse, Equiangular, Equilateral, Isosceles, Scalene triangles.
Corresponding Angles
Angles of two triangles with matched vertices.
Congruent Triangles
Triangles with matching vertices and congruent corresponding parts.
SSS Congruence Postulate
Triangles are congruent if three sides are equal.
SAS Congruence Postulate
Triangles are congruent if two sides and the included angle are equal.
ASA Congruence Postulate
Triangles are congruent if two angles and the included side are equal.
AAS Congruence Postulate
Triangles are congruent if two angles and a non-included side are equal.
Points Postulate
ā A line contains at least two points.
ā A plane consists of at least three non-collinear points.
ā A space contains at least four non-coplanar points.
Line Postulate
Two points determine a line.
Plane Postulate
Three non-collinear points determine a plane.
Flat Plane Postulate
If two points of a line lie on the plane, then the entire line lies on the plane.
Plane Intersection Postulate
If two planes intersect, then their intersection is a line.
Ruler Postulate
For every pair of points, there is only positive real number called the distance between the two points.
Segment Construction Postulate
On any ray, there is exactly one point at a given distance from the endpoint of the ray.
Segment Addition Postulate
Midpoint Postulate
A segment has exactly one midpoint.
Line Intersection Theorem
If two lines intersect, then their intersection is exactly one point.
Line-Point Theorem
Given a line and a point not on the line, there is exactly one plane that contains them.
Line-Plane Theorem
Given two intersecting lines, there is exactly one plane that contains the two lines.
Line-Plane Intersection Theorem
Given a plane and a line not on the plane, their intersection is one and only one point.
Note
Flashcard