Identify the Property which supports each

Conclusion

IF

then

AB BC

BC AB

Symmetric Property of Congruence

A A

Reflexive Property of Congruence

IF

and

then

AB BC

BC CD

AB CD

Transitive Property of Congruence

180m A m B If

and90m B 90 180m A then

Substitution Property of

Equality

IF

AB = CD

Then

AB + BC = BC + CD

Addition Property of Equality

If AB + BC= CE

and CE = CD + DE

then

AB + BC = CD + DE

Transitive Property of Equality

If

AC = BD

then

BD = AC.

Symmetric Property of

Equality

If AB + AB = AC

then 2AB = AC.

Distributive Property

m B m B

Reflexive Property of Equality

If

2(AM)= 14

then

AM=7

Division Property of Equality

If

AB + BC = BC + CD

then

AB = CD.

Subtraction Property of

Equality

If

AB = 4

then

2(AB) = 8

Multiplication Property of

Equality

Let’s see if you remember a few oldies but goodies...

If B is a point between A and C, then

AB + BC = AC

The Segment Addition Postulate

If Y is a point in the interior of

then

RST

m RSY m YST m RST

Angle Addition Postulate

IF M is the Midpoint

of

then

AB

.AM MB

The Definition of Midpoint

IF

bisects

then

AB

CADCAB BAD

The Definition of an Angle Bisector

If AB = CD

then

AB CD

The Definition of Congruence

If

then

is a right angle.

90m AA

The Definition of Right Angle

1

If

is a right angle, then the lines are perpendicular.

1

The Definition of Perpendicular

lines.

If

Then

A B

m A m B

The Definition of Congruence

And now a few new ones...

If and are right angles,

then

A B

A B

Theorem: All Right angles are congruent.

1 2

If and are congruent, then lines m and n are perpendicular.

n

m

1 2

Theorem: If 2 lines intersect to form congruent adjacent angles, then the lines are perpendicular.

If and are complementary, and and are complementary, then

AA

B

C

B C

Theorem: If 2 angles are complementary to the same angle, they are congruent to each other.

1 2

Then 1 2 180m m

The Linear Pair Postulate

(The angles in a linear pair are supplementary.)

1 2Then

1 2

Theorem:

Vertical Angles are congruent.

The End