Download Unit 1 Lesson 2 Properties and Theorems

Advanced Math I
Unit 1 Lesson 2 Properties, Definitions & Theorems
m
l
Transitive Property of Equality: If a = b and b = c, then a = c.
Ex:
If
1  2 and
2  3 then 1  3
1
c
d
3
2
Substitution: If a = b and a + c = d, then b + c = d. It doesn’t have to be addition. It works any time you
have congruent variables and you replace one of them with the other.
Ex:
1  3 and
1  2  180
so 3  2  180
c
Congruent: same measure.  
Ex: m1  70 and m3  70 so 1  3 .
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1
3
2
d
Supplementary Angles: Two angles whose sum is 180 . They do not have to be
adjacent.
Ex: 1 & 2 and 3 & 2
c
d
Vertical Angles: Angles that are opposite one another when lines intersect.
Ex: ACB & DCE
Vertical Angles Theorem: Vertical angles are congruent.
Ex: ACB  DCE

Linear Pair: Angles that are adjacent to one another when lines intersect.
Ex: ACD & DCE
Linear Pair Property: If two angles are a linear pair, then the sum of their
measures is 180.
Ex: ADB BDC 180


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1
2
3
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Supplementary Angles: Two angles whose sum is 180 . They do not have to be
adjacent.
Ex: 1 & 2 and 3 & 2
1
c
3
2
d
E
Parallel Line Postulate: In a plane, two lines cut by a transversal are parallel if and
only if corresponding angles have the same measure.
Ex: AB //CD iff EGB  GHD
A
G
C
B
H

D
I
From the Parallel Line Postulate we can prove the following:
 Two lines cut by a transversal are parallel if and only if a pair of interior angles
on the same side of the transversal are supplementary.
Ex: AB //CD iff AGH  GHC  180
E
A
G
C
B
H

D
I
 Two lines cut by a transversal are parallel if and only if a pair of exterior
angles on the same side of the transversal are supplementary.
Ex: AB //CD iff EGB  DHI  180
E
A
G
C
B
H
D

I
 Two lines cut by a transversal are parallel if and only if a pair of alternate
interior angles have the same measure.
Ex: AB //CD iff AGH  GHD
E
A
G
C

H
E
A
 Two lines cut by a transversal are parallel if and only if a pair of alternate
B
G
D
B
I
C
H
I
D
exterior angles have the same measure.
Ex: AB //CD iff EGB  CHI

Perpendicular Lines: Lines that intersect and form right angles 90  .  
Ex: m  n
n
m
Angle Addition Postulate: The sum of two or more adjacent angles is equal to the larger angle that they
form.
Ex:
A
C
B
D
The sum of a triangle’s interior angles is 180.
Ex: A  B  C  180
C

A
B
Exterior Angle Theorem for a Triangle: The measure of the exterior
angle of a triangle is congruent to the sum of the two interior angles that are
not adjacent to the exterior angle.
Ex: 4  1 2
2
1
3
4