Math proofs vocabulary

Definition of Congruence

Agreement, harmony or matching up completely (congruent)

Definition of an Angle Bisector

A line, ray, or line segment that divides an angle into two equal, congruent smaller angles

Definition of a Segment Bisector

Any point, line, ray, or line segment that divides another line segment into two equal halves

Definition of Complementary Angles

Two angles whose sum equals to 90 degrees

Definition of Supplementary Angles

Two angles whose measures add up to exactly 180 degrees

Definition of Perpendicular

Two lines or surface that meet at a 90 degree right angle, forming an “L” or “T” shape

Definition of a Right Angle

An angle that measures exactly 90 degrees, forming a square corner

Definition of a Midpoint

exact middle point of a line segment that is equally distant from both ends

Angle Addition Postulate

If a point or ray lies inside an angle, the sum of the two smaller adjacent angles equals the measures of the whole/larger angle

Segment Addition Postulate

If point B lies between points A and C on a line segment, the sum of the lengths of the two smaller segments equal the length of the entire segment

Vertical Angles Theorem

The opposite angles formed when two straight lines intersect are equal (congruent)

Congruent Complements Theorem

If two angles are complementary to the same angle (or to congruent angles), then those two angles are congruent

Congruent Supplements Theorem

If two angles are supplementary to the same angle (or two congruent angles), then those two angles are congruent

Linear Pairs Theorem

If two angles form a linear pair, their measures always add up to 180 degrees

Complements Theorem

If the non-common sides of two adjacent angles form a right angle, then the two angles are complementary angles Complementary Angles Theorem

Supplements Theorem

If two angles form a linear pair, then they are supplementary angles

Right Angle Congruence Theorem

All right angles are congruent to each other because they all measure 90 degrees

Transitive Property

If a first value relates to a second value, and that second value relates to a third value in the same way, then the first and third value also relate to each other

Addition Property

basic rules that show how numbers behave when added together

Subtraction Property

If you subtract the same value from both sides of an equation, the two sides remain equal

Multiplication Property

If you multiply both side of an eqaution by the same number, the sides remain equal

Division Property

If you divide both sides of a true equation by the same non-zero number, the two sides remain equal

Reflexive Property

Any geometric figure, line segment, or angle is always congruent/equal in size and shape to itself

Symmetric Property

You can swap the left and right side of an equation or congruence statement without changing its truth (if a=b, then b=a) (if x=12, then 12=x)