proofs

Reflexive Property of Equality

AC=AC

Symmetric Property of Equality

If AC=BC then BC=AC

Transitive Property of Equality

If X=Y and Y=Z then X=Z

Addition Property of Equality

If X=Y then X+Z=Y+Z

Subtraction Property of Equality

If X=Y then X-Z=Y-Z

Multiplication Property of Equality

If X=Y then X(Z)=Y(Z)

Division Property of Equality

If X=Y then X/Z=Y/Z (z cannot be zero)

Substitution Property of Equality

If X=Y then Y can be substituted for X in any expression or X can be substituted for Y in any expression.

Distributive Property of Equality

If X(Y+Z)=XY + XZ

Reflexive Property of Congruence

<A ≅ <A

Symmetric Property of Congruence

If <A ≅ <B, then <B ≅ <A

Transitive Property of Congruence

If ∠A≅∠B, and ∠B≅∠C,
then ∠A≅∠C

Vertical Angles Theorem

when it’s an X and one side is x2 and the other is 60

Linear Pair Postulate

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

Definition of Angle Bisector

A ray that divides an angle into two congruent angles

Angle Addition Postulate

If R is in the interior of <PQS, then m<PQR + m<RQS = m<PQS

Definition of Complementary Angles

Two positive angles whose sum is 90*

Definition of Supplementary Angles

Two positive angles whose sum is 180*

Segment Addition Postulate

If B is between A and C, then AB + BC= AC

Congruent Supplements Theorem

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

Right Angle Congruence Theorem

All right angles are congruent.

Definition of Right Angle

An angle with a measure equal to 90 degrees.

Definition of Congruent Angles

Angles that have the same measure.

Definition of Congruent Segments

Segments that have the same length.

Definition of midpoint.

The point that divides a segment into two congruent segments.

Definition of a Linear Pair

Two adjacent angles whose non-common sides are opposite rays.

Definition of a Segment Bisector

A point, ray, line, segment, or plane that divides a segment into two congruent segments.

Definition of Vertical Angles

Two angles whose sides form two pairs of opposite rays

Definition of Perpendicular Lines

Two lines that intersect to form a right angle.

Congruent Complements Theorem

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