Geometry- properties of proofs

Simplify/CLT

4h+9+2h=15 6h+9=15

Reflective Property of Congruence

AB=AB

Definition of Angle Bisector

An angle bisector divides an angle into two equal parts

Reflexive Property of Equality

For any real number a, a=a 6y=6y

Segment Addition Postulate

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

Transitive Property of Congruence

If AB ≅ CD and CD ≅ EF, then AB ≅ EF.

Definition of Congruence

If EF ≅ CD, then EF = CD

Definition of Congruence

If GH ≅ CD, then GH = CD

Distributive Property of Equality

If a (b + c) then ab + ac 8(2+10)=c 16+80=c

Transitive Property of Equality

If a=b and b=c, then a=c if 4d=5s and 5s= 8, then 4d=8

Substitution Property of Equality

If a=b, then a may be replaced by b in any equation or expression. 14n + 7= 35 n=2 14(2)+ 7= 35

Addition Property of Equality

If a=b, then a+c=b+c 5m-5=20 5m=25

Subtraction Property of Equality

If a=b, then a-c=b-c 4a+8=7 4a=1

Multiplication Property of Equality

If a=b, then ac=bc if n=2, then 5n=10

Congruent Supplements Theorem

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

Definition of Perpendicular

Perpendicular lines form right angles

Definition of Complementary Angles

Two angles are complementary if their sum is 90 degrees. measure angle 4 + measure angle 5= 90 degrees, then angle 4 and angle 5 are complementary.

Angle Addition Postulate

for any angle, the measure of the whole is equal to the sum of the measures of its parts

Symmetric Property of Congruence

if DF= AE, then AE= DF

Definition of Midpoint

if H is the midpoint of RG then RH=HG

Division Property of Equality

if a = b then a/c = b/c if 4x=28 then x=7

Symmetric Property of Equality

if a=b, then b=a if 4x=y then y=4x

Congruent Complements Theorem

if angle 3 is complementary to angle 4 and angle 4 is complementary to angle 5, then angle 3 ≅ angle 5

Vertical Angles Theorem

if angle 6 and angle 8 are vertical angle, then angle 6 ≅ 8

Definition of Supplementary Angles

if angle H and angle Q are supplementary, then measure angle H and measure angle Q= 180 degrees.

Complement Theorem

if angle J and angle K form a right angle, then angle J and angle K are complementary.

Linear Pair Theorem

if angle T and angle P form a linear pair, then angle T and angle P are supplementary.

Definition of a Right Angle

measure angle K= 90 degrees, then angle K is a right angle