Geometry Basic Definitions

All definitions must be written in “If ... then ...” form in

An angle is made up of two rays (sides) with a common endpoint (vertex).

An acute angle is an angle whose measure is greater than 0° and less than 90°.

A right angle is an angle whose measure is 90°.

An obtuse angle is an angle whose measure is greater than 90° and less than 180°.

A straight angle is an angle whose measure is 180°.

≅ Congruent angles are angles that have the same measure. ≅ Congruent segments are segments that have the same length. Points that lie on the same line are called collinear.

A theorem is a mathematical statement that can be proved.

The midpoint of a segment is a point that divides the segment into two congruent M segments.

A point (or segment, ray or line) that divides a segment into two congruent segments M bisects the segment.

Two points (segments, rays or lines) that divide a segment into three congruent A B segments trisect the segment. The two points at which the segment is divided are called the trisection points of the segment.

The bisector of an angle is a ray that divides the angle into two congruent angles. (The ray is said to bisect the angle )

Two rays that divide an angle into three congruent angles trisect the angle. The two dividing rays are called trisectors of the angle.

A postulate is an unproved assumption.

A definition states the meaning of a term or idea.

Union: The set of all elements contained in two sets. ∪

Intersection: The set of all elements common to two set. ∩

Empty Set: The set containing no elements. ∅ Betweenness: If a point is between two other points, then the three points are collinear and the sum of the measures of the smaller segments formed by the three points is equal to the measure of the longest segment. (A-B-C ⇒ AB + BC = AC)

Triangle Inequality: If three points are non-collinear, then the sum of the lengths of any two sides is greater than the length of the third side. (AB + BC > AC, BC + AC > AB, and AC + AB > BC)

Angle Addition: If two angles are adjacent angles then the sum of the measures of the two smaller angles is equal to the measure of the larger angle. (If X is in the interior of ∠PAQ, then m∠PAQ = m∠PAX + m∠XAQ)

Probability: Probability = number of winners number of possibilities

Theorems:

If two angles are right angles, then they are congruent.

If two angles are straight angles, then they are congruent.

Postulate:

Two points determine a line.

Logic and Reasoning:

Conditional sentence: p ⇒ q Converse: q ⇒ p Inverse: ∼p ⇒ ∼q Contrapositive: ∼q ⇒ ∼p

If a conditional sentence is true then the contrapositive is true.

Chain of reasoning: If p ⇒ q and q ⇒ r, then p ⇒ r

Also: A complete rotation about a point is 360°