Angle Proofs Flashcards

Definition of Congruence

m<A = m<B <--> <A congruent to <B

Definition of Angle Bisector

an angle bisector divides an angle into two equal parts.

Definition of Complementary Angles

Complementary <--> sum is 90 degrees

Definition of Supplementary Angles

Supplementary <--> sum is 180 degrees

Definition of Perpendicular

Perpendicular lines form right angles

Definition of a Right Angle

A right angle = 90 degrees

Angle Addition Postulate

m<ABD + m<DBC = m<ABC

Vertical Angles Theorem

If two angles are vertical, then they are congruent.

Complement Theorem

If two angles form a right angle, then they are complementary
Right Angle --> Complementary

Supplement Theorem

If two angles form a linear pair, then they are supplementary
Linear Pair --> Supplementary

Congruent Complements Theorem

If <A is complementary to <B and <C is complementary to <B, then <A is congruent to <C

Congruent Supplements Theorem

If <A is supplementary to <B and <C is supplementary to <, then <A is congruent to <C

Reflexive Property of Congruence

For any segment AB, segment AB is congruent to segment AB

Symmetric Property of Congruence

If segment AB is congruent to segment CD, then segment CD is congruent to segment AB

Transitive Property of Congruence

If segment AB is congruent to CD and segment CD is congruent to segment EF, then segment AB is congruent to segment EF

Addition Property of Equality

If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal.

Subtraction Property of Equality

You can subtract the same number from both sides of an equation and get an equivalent equation.

Multiplication Property of Equality

When we multiply both sides of an equation by the same number, the two sides remain equal.

Division Property of Equality

If both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal.

Distributive Property of Equality

Multiplying a quantity by the sum of two or more terms is the same as adding together the products of the original quantity and each term.

Substitution Property of Equality

If a variable x is equal to another variable y, then x can be substituted in place of y in any equation/expression and y can be substituted in place of x in any equation/expression.

Reflexive Property of Equality

a number is always equal to itself. If a is a number, then. a = a. a=a.

Symmetric Property of Equality

we can interchange the sides of an equation without changing the truth-value of the equation. That is, if a = b, then b = a.

Transitive Property of Equality

If x = y and y = z, then x = z.