proof words

Deductive Reasoning

A process of using evidence (assumptions and proven facts like postulates and theorems) to support certain statements. This will proof a statement to be true.

Postulate

A statement that is assumed to be true without proof.

Theorem

A statement that can be proven by using deductive reasoning.

Direct Proof

This type of proof will start with given statements. Then, you must use logic and knowledge to arrive at the proven statement.

Reflexive Postulate

A quantity is equal to itself.

Ex. Line segment AB is congruent to line segment AB.

Symmetric Postulate

If a=b, then b=a.

Transitive Postulate

If a=b and b=c, then a=c.

Substitution Postulate

A quantity can be substituted for its equal in any given expression.

Partition Postulate

The whole is equal to the sum of its parts.

Addition Postulate

If equal quantities are added to equal quantities, then the sums are equal.

Subtraction Postulate

If equal quantities are subtracted from equal quantities, then the differences are equal.

Multiplication Postulate

If equal quantities are multiplied by equal quantities, then the products are equal.

Division Postulate

If equal quantities are divided by equal quantities, then the quotients are equal.

SSS Postulate

If three sides of one triangle are congruent to the corresponding three sides of another triangle, then the two triangles are congruent.

--> This is because SSS≅SSS.

SAS Postulate

If two sides and the included angle of one triangle are congruent to the corresponding two sides and the included angle of another triangle, then the triangles are congruent.

--> This is because SAS≅SAS.

ASA Postulate

if two angles and the included side of one triangle are congruent to the corresponding two angles and the included side of another triangle, then the triangles are congruent.

--> This is because ASA≅ASA.

Included Angle

An angle that is formed by two sides that share a common vertex.

Ex. Angle B is formed by line segment AB and line segment BC.

Included Side

A side that is formed by connecting two angles together.

Ex. Angle A and angle B create the line segment or side AB.

Theory Number 1

All right angles are congruent to each other.

Theory Number 2

Supplements or complements of the same angle are congruent.

Theory Number 3

Supplements or complements of congruent angles are congruent.

Theory Number 4

If two angles form a linear pair, then they are supplementary (add up to 180 degrees).

Theory Number 5

If two angles are vertical angles, they they are congruent.

Midpoint

A point that divides a line segment into two congruent segments.

Bisector of Line Segment

A line or line segment that intersects a line segment at its midpoint to create two congruent segments.

Bisector of an Angle

A ray whose endpoint is the vertex of the angle and divides the angle into two congruent angles.

Perpendicular Lines

Lines that intersect each other to form right angles (90 degrees).

Perpendicular Bisector

A line that intersects the midpoint of a line segment and is perpendicular to that line segment (creating right angles). At the same time, this line will divide the line segment into two congruent segments.

Median

A line drawn from any vertex of a triangle to the midpoint of the opposite side.

Altitude

A line drawn from any vertex of a triangle and to the opposite side however, this line must be perpendicular (forms right angles) to the opposite side.