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1

Point

is a location in space represented by a dot with no dimension, named with a capital letter.

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2

Line

is a one-dimensional object with no width, extending infinitely in both directions, named by a lowercase letter or two points on it.

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3

Plane

is a flat, two-dimensional surface extending infinitely, with no thickness, named by a capital script letter or three non-collinear points.

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4

Postulates

Statements accepted as true without proof.

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5

Theorems

Statements proven true using undefined terms, definitions, postulates, and other theorems.

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6

Supplementary Angles

Two angles with a sum of 180°.

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7

Complementary Angles

Two angles with a sum of 90°.

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8

Adjacent Angles

Two angles sharing a vertex and side but no interior points.

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9

Linear Pair of Angles

Adjacent angles with non-common sides forming a straight line, summing to 180°.

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10

Vertical Angles

Pair of congruent angles opposite each other formed by intersecting lines.

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11

Types of Triangles

Right, Acute, Obtuse, Equiangular, Equilateral, Isosceles, Scalene triangles.

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12

Corresponding Angles

Angles of two triangles with matched vertices.

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13

Congruent Triangles

Triangles with matching vertices and congruent corresponding parts.

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14

SSS Congruence Postulate

Triangles are congruent if three sides are equal.

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15

SAS Congruence Postulate

Triangles are congruent if two sides and the included angle are equal.

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16

ASA Congruence Postulate

Triangles are congruent if two angles and the included side are equal.

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17

AAS Congruence Postulate

Triangles are congruent if two angles and a non-included side are equal.

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18

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.

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19

Line Postulate

Two points determine a line.

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20

Plane Postulate

Three non-collinear points determine a plane.

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21

Flat Plane Postulate

If two points of a line lie on the plane, then the entire line lies on the plane.

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22

Plane Intersection Postulate

If two planes intersect, then their intersection is a line.

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23

Ruler Postulate

For every pair of points, there is only positive real number called the distance between the two points.

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24

Segment Construction Postulate

On any ray, there is exactly one point at a given distance from the endpoint of the ray.

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25

Segment Addition Postulate

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26

Midpoint Postulate

A segment has exactly one midpoint.

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27

Line Intersection Theorem

If two lines intersect, then their intersection is exactly one point.

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28

Line-Point Theorem

Given a line and a point not on the line, there is exactly one plane that contains them.

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29

Line-Plane Theorem

Given two intersecting lines, there is exactly one plane that contains the two lines.

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30

Line-Plane Intersection Theorem

Given a plane and a line not on the plane, their intersection is one and only one point.

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