Geometry - Definitions

Point

Point

Represents location, no dimension (is collinear or forms a triangle)

Line

Infinite collection of at least 2 points

Line Segment

Portion of a line, 2 endpoints

Ray

Portion of a line, 1 endpoint, extends infinitely in other direction

Angle

Union of 2 rays

Triangle

Union of 3 line segments (Sum of lengths of any 2 sides are ALWAYS > 3rd side, sides can’t equal 0)

Union

Set of all points in one object or the other (everything together)

Intersection

Set of all points in one object and the other (overlap)

Postulate (Axiom)

Acceptance of truth, not provable

Segment Addition Postulate

Length of line segment = sum of smaller pieces inside

Angle Addition Postulate

Measure of angle = sum of smaller angles inside

Congruent

Equal in length/measure

Acute Angle

Angle measure = 0 < A < 90

Obtuse Angle

Angle measure = 90 < A < 180

Right Angle

Angle measure = 90

Straight Angle

Angle measure = 180

Collinear

Points in/on a straight line

Betweenness

A point is between 2 points only if all 3 are collinear

Bisection

Point/line/line segment/ray divides a segment into 2 congruent segments

Midpoint

Bisection point of a segment, only ever 1 midpoint

Trisection

Point/line/line segment/ray divides segment into 3 congruent segments

Perpendicularity

Objects/segments/lines that form right angles (Converse - Right angles are formed by perpendicular segments)

Complementary Angles

2 angles whose sum is 90 degrees

Supplementary Angles

2 angles whose sum is 180 degrees

Adjacent Angles

Angles sharing a common ray

Linear pair

2 angles that form a straight line

Vertical Angles

Angles opposite of each other

Transformation

A change in a figures orientation

Rigid Transformation

A transformation that doesn’t change a figures image

Preimage

The original figure in a transformation

Image

The new figure in a transformation

Translation

Every point of an object is moved the same fixed distance and direction

Rotation

An object is rotated about a fixed point

Reflection

All points of an object are reflected (flipped) on axis of symmetry

Vector

Quantity with both direction and magnitude, <x, x>

Deductive Structure

A system of thought in which conclusions are justified by means of previously proved statements

Conditional Statement

If … p, then … q p → q

Converse

If … q, then … p q → p

Biconditional

Both the conditional statement and converse are true

Inverse

If not … p, then not … q ~p → ~q

Contrapositive

If not … q, then not … p ~q → ~p

Theorem

Mathematical statement that can be proved