Geometry Exam #2: Basic Geometry

Primitive Notions

Terms we don't need to define because everyone accepts them as true

Point

A position or location

Lines

A set of points that extend indefinitely in two directions

Plane

Three or more points that form a flat 2-D surface

Collinear

two or points that lie on the same line

Coplanar

three or more points that lie on the same plane

Postulate

a statement that doesn't need to be proved, everyone accepts it to be true, IS used for reasoning within proofs

Theorum

a statement that CAN be proven using definitions, postulates, and other theorems

The Partition Postulate

The whole is equal to the sum of its parts

Congruent

two objects that have the same measure

Midpoint

a point that divides that segment into two congruent parts

Bisector :

a segment that intersects the line segment at its midpoint

The Substitution Postulate

Any quantity can be substituted for it's equal in an expression [Only works with equalities]

Relation

An association between two or more objects

Reflexive Property

Any object associated with itself

Symmetric Property

if a is associated with b, then b is associated with a

Transitive Property

if a is associated with b, and b is associated with c, then a is associated with c

Equivalence Property

When all three properties are satisfied at the same time

The Addition Postulate

When equal quantities are added to equal quantities then the sums are equal.

The Subtraction Postulate

When equal quantities are subtracted from equal quantities then the difference are equal.

The Multiplication Postulate

When equal quantities are multiplied by equal quantities then the products are equal.

The Division Postulate

When equal quantities are divided to equal quantities then the quotients are equal.

Midpoint Theorem

The midpoints of a line segment divides that segment into two segments half as long as the original one

Angle Bisector

The bisector of an angle divides that angle into two angles half the measure of the original

Complementary

two angles that add up to 90 degrees

Supplementary

two angles that add up to 180 degrees

Linear Pairs

Two angles that form a linear iff they are adjacent angles that are supplementary

Supplementary Angle Theorem

if two angles form a linear pair, they are supplementary

Perpendicular

two lines are perpendicular iff they intersect to form right angles

Congruent Complementary Angle Theorem

if two angles are complementary to the same angle then they are congruent

Congruent Supplementary Angle Theorem

if two angles are supplementary to the same angle then they are congruent

Perpendicular Line Theorem

if two lines intersect to congruent adjacent angles, then the lines are perpendicular

Corollaries

Theorems in the "same" proofs as other theorems

Congruent Vertical Angle Theorem

if two angles are vertical angles, then they are congruent.

Vertical Angles

Angles formed with intersecting lines, iff the sides of one angle are opposite the rays of the side of the other angle

Proof By Contradiction

Claiming the opposite of the statement we need to prove to prove that any other way is wrong so thus the original statement has to be correct.