MATH Q4

Point

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 180°.

Complementary Angles

Two angles with a sum of 90°.

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 180°.

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

● A line contains at least two points.

● A plane consists of at least three non-collinear points.

● 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.