Proofs

Given

Information that’s provided

Addition Property

If a=b, then a+c = b+c

Subtraction Property

If a=b, then a-c = b-c

Multiplication Property

If a=b, then a*c=b*c

Division Property

If a=b, then a/c=b/c

Distributive Property

If a(b+c), then a(b+c) = a*c+b*c

Substitution Property

If a=b then a may be replaced by b in any expression or equation

Reflexive Property

For any real number a. a=a (A value will always equal itself)

Symmetric Property

If a=b, then b=a

Transitive Property

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

Simplification

Combining like terms

Reflexive Property of Congruence

For any segment AB, Line AB ≅ Line AB

Symmetric Property of Congruence

If Line AB ≅ Line CD, then Line CD ≅ Line AB

Transitive Property of Congruence

If Line AB ≅ Line CD, and Line CD ≅ Line EF, then Line AB ≅ Line EF

Definition of Congruence

Segments are congruent if and only if they have the same measure. If line AB ≅ Line CD, then AB=CD, and If AB=CD, then Line AB ≅ Line CD

Definition of Midpoint

The midpoint of a segment divides the segment into two congruent parts.

Segment Addition Postulate

If A, B, and C are collinear points and B is between A and C, then AB+BC=AC.

Definition of Congruence (Angles)

The measures of two angles are equal if and only if the angles are congruent. m∠A=m∠B⇿∠A≅∠B

Definition of Right Angle

An angle measures 90° if and only if it is a right angle. m∠A=90°⇿∠A is a right angle

Definition of Complimentary Angles

Two angles are complementary if and only if the sum of their measures is 90°.

Definition of Supplementary Angles

Two angles are supplementary if and only if the sum of their measures is 180°.

Definition of an Angle Bisector

An angle bisector divides an angle into two equal parts.

Definition of Perpendicular

Perpendicular lines form right angles.

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 complimentary.

Linear Pair Theorem

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

Congruent Complements Theorem

If two angles are complementary to the same angle, then they are congruent. If ∠A is complementary to ∠B, and ∠C is complementary to ∠B, then ∠A≅∠C

Congruent Supplements Theorem

If two angles are supplementary to the same angle, then they are congruent. If ∠A is supplementary to ∠B, and ∠C is supplementary to ∠B, then ∠A≅∠C