# Theorems and Postulates

Ηλεκτρονική - Συσκευές

10 Οκτ 2013 (πριν από 4 χρόνια και 9 μήνες)

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Theorems and Postulates

Chapter 1

A

C

AB + BC = AC

C

m

ACB + m

BCD = m

ACD

Chapter 2

Law of Detachment p

q

Law of Syllogism

p

q and q

r

then p

r

a = b then a+c = b+c

Subtraction Property If a = b then a

c = b

c

Multiplication Property If a = b then ac = bc

Division Property If a = b and c

0 then a

c = b

c

Reflexive Property a = a,

, and

ABC

ABC

Symmetric Property If a = b, then b = a, If

then

If

A

B then

B

A

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

If

A

B and

B

C then

A

C

Substitution Property If a=b, then a can be substituted for b in any equation or expression

Right Angle Congruence Theorem

All
right a
ngles are con
gruent

B

A

B

D

Congruent Supplements Theorem

If 2 angles are supplementary to the same angle then

The 2 angles are congruent

Congruent Complements Theorem
-

If 2 angles are complementary to the same angle
then the 2 angles are congruent

Linear Pair Po
stulate

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

Vertical Angle Theorem

Vertical angles are congruent

Chapter 3

Parallel Postulate

If there is a line and a point not on the line, then there is exactly one

Line thr
ough the point that is parallel to the given line.

Perpendicular Postulate
-

If there is a line and a point not on the line, then there is exactly

one line through the point that is perpendicular to the given line.

Corresponding Angles Postulate

If parallel lines are cut by a transversal, then the

corresponding angles are congruent.

Alternate Interior Angles
-

If parallel lines are cut by a transversal, then the alternate

interior angles are congruent.

Alternate Exterior An
gles
-

If parallel lines are cut by a transversal, then the alternate

exterior angels are congruent.

Consecutive Interior Angles
-

If parallel lines are cut by a transversal, then the

consecutive interior angles are supplementary.

Perpend
icular Transversal

If a transversal is perpendicular to one of the two parallel

lines, then it is perpendicular to the other.

Corresponding Angles Converse

If two lines are cut by a transversal so

that the corresponding ang
les are

congruent, then the lines are parallel.

Alternate Interior Angles Converse

If two lines are cut be a transversal so that the

alternate interior angles are congruent, then the lines

are parallel.

Consecutive Interior Angl
es Converse

If two lines are cut by a transversal so that the

consecutive interior angles are supplementary

then the lines are parallel.

Alternate Exterior Angles Converse

If two lines are cut be a transversal so that the

alt
ernate
exterior

angles are

congruent, then the

lines ar
e parallel.

Duel Parallel Line Theorem

If two lines are parallel to the same line then the lines are

parallel.

Duel Perpendicular Line Theorem

If two lines are perpendicular to the same

line then

the lines are parallel.

Lines that are parallel have the same slope.

Lines that are perpendicular have slopes that are the negative reciprocal of each other.

Chapter 4

Triangle Sum Theorem

the sum of the three interior angl
es of a triangle equal 180

.

Exterior Angle Theorem

the exterior angle of a triangle is equal to the sum of the 2

remote interior angles.

Third Angle Theorem

If 2 angles of one triangle are congruent to 2 angles of another

triangle th
en the third angles are congruent.

Side

Side

Side (SSS) Congruence

If 3 sides of one triangle are congruent to the

corresponding sides of another triangle, then the

2 triangles are congruent.

Side

Angle

Side (SAS) Congruence

If two sides and the included angle of one

triangle are congruent
to the corresponding

sides and included angle of another triangle,

then the triangles are congruent.

Angle

Side

Angle (ASA) Congruence
-

If two angles and the included side of one

triangle are congruent to the corresponding

angles and included side of another triangle,

then the triangles are congruent.

Angle

Angle

Side (AAS) Congruence
-

If two angles and the nonincluded side of one

triangle are congruent to the corresponding

angles and nonincluded side of another triangle,

then the triangles are congruent.

Base Angle Theorem

If 2 sides of

a triangle are congruent, then the angles opposite

them are congruent.

Converse of the Base Angle Theorem

If 2 angles of a triangle are congruent, then the

sides opposite them are congruent.

If a triangle is equilateral, then it is equia
ngular.

If a triangle is equiangular, then it is equilateral.

Hypotenuse

Leg (HL) congruence

If the hypotenuse and a leg of a right triangle are

congruent to the hypotenuse and corresponding leg

of a second right triangle, then the triang
les are

congruent.