Proof Reasons- Geometry

Definition of a Midpoint

A point B is called a midpoint of a segment AC if B is between A and C and AB=BC

Definition of Congruent Angles

If m<ABC=m<DEF, then <ABC is cong. to <DEF

Definition of an Angle Bisector

If ray EB intersects <DEF, and m<DEB=m<BEF, then ray EB is an angle bisector

Distributive POE

a(b+c)=ab+ac

Right Angle Congruence Theorem

all right angles are congruent

Segment Addition Postulate

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

Angle Addition Postulate

if P is in the interior of <RST, then m<RST=m<RSP+m<PST

Substitution POE

if a=b, and c is not equal to 0, then a can be substituted for b in any equation or expression

Division POE

if a=b, and c is not equal to 0, then a/c=b/c

Addition POE

if a=b, then a+c=b+c

Subtraction POE

if a=b, then a-c=b-c

Multiplication POE

if a=b, then ac=bc

Definition of Perpendicular Lines

if lines AB and CD intersect to form a right angle, then they are perpendicular lines. If AB and CD are perpendicular lines, then they intersect to form a right angle

Definition of supplementary Angles

if m<ABC+m<DEF=180 degrees, then they are supplementary angles. If <ABC and <DEF are supplementary angles, then they sum to 180 degrees

Definition of Complementary Angles

if m<ABC+m<DEF=90 degrees, then they are complementary angles. If <ABC and <DEF are complementary angles, then they sum to 90 degrees

Definition of Right Angles

if m<ABC=90 degrees, then it is a right angle. If <ABC is a right angle, then m<ABC=90 degrees

Definition of a Segment Bisector

if point B is between points A and C, and AB=BC, then B bisects the segment AC

Definition of Congruent Segments

if the length of segment AB=the length of segment BC, then segments AB and BC are congruent

Congruent Complements Theorem

if two angles are complementary to the same angle or to congruent angles, then they are congruent

Congruent Supplements Theorem

if two angles are supplementary to the same angle or to congruent angles, then they are congruent

Linear Pair Postulate

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

Reflexive POE

real number: for any real number a, a=a segment length: for any segment AB, AB=AB angle measure: for any angle A, m<A=m<A

Symmetric POE

real number: for any real numbers a and b, it a=b then b=a segment length: for any segments AB and CD, if AB=CD then CD=AB angle measure: for any angles A and B, if m<A=m<B then m<B=m<A

Transitive POE

real numbers: for any real numbers a, b, and c, if a=b and b=c, then a=c segment length: for any segments AB, CD, and EF, if AB=CD and CD=EF, then AB=EF angle measure: for any angles A, B, and C, if m<A=m<B and m<B=m<C, then m<A=m<C

Reflexive POC

segments: for any segment AB, AB is cong. to AB angles: for any angle A, <A is cong. to <A

Symmetric POC

segments: for any segments AB and CD, if AB is cong. to CD, then CD is cong. to AB angles: for any angles A and B, if <A is cong. to <B then <B is cong. to <A

Transitive POC

segments: for any segments AB, CD, and EF, if AB is cong. to CD and CD is cong. to EF, then AB is cong. to EF angles: for any angles A, B, and C if <A is cong. to <B and <B is cong. to <C, then <A is cong. to <C

Vertical Angles Congruence Theorem

vertical angles are congruent