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Geometry
Chapter 2
LESSON 2.5 ANGLE
RELATIONSHIPS
Linear Pair Conjecture C-1
 If two angles form a linear pair, then
the measure of the angles add up to 180
degrees.
.
Vertical Angles Conjecture C-2
 If two angles are vertical angles, then
they have equal measures (are congruent).
3
2
4
1
Measure of angle 1 equals
the measure of angle ______.
While the Measure of angle 2
equals the measure of angle
______.
Putting C-1 and C-2 Together
 Example Problems: Solve for the missing
variables.
130
50 x
y
130
46

48
b
86
a
cd

86 
46
48
z 50
Solution:
x + 130 = 180 (C-1)
-130 -130
x = 50
**Use C-2 to solve for y and z.
Solution:
48 + a + 46 = 180 (Conjecture???)
a + 94 = 180
- 94 - 94
a = 86
**Use C-2 to solve for b,c,and d.
CHAPTER 2
LESSON 2.6
SPECIAL ANGLES ON PARALLEL LINES
PARALLEL LINES CONJECTURE C-3
 If two parallel lines are cut by a transversal, then
corresponding angles are… CONGRUENT,
alternate interior angles are… CONGRUENT,
and alternate exterior angles are… CONGRUENT.
KEY: Lines
must be proven
parallel.
Corresponding Angles Conjecture C-3a
(CA Conjecture)
 If two parallel lines are cut by a transversal, then
corresponding angles are ____________
CONGRUENT.
1
2
Angle 1 is congruent to angle 2.
They are corresponding angles.
52 degrees
Therefore, if angle 1 is 52 degrees, then angle 2 is __________.
Alternate Interior Angles Conjecture C-3b
(AIA Conjecture)
 If two parallel lines are cut by a transversal, then
CONGRUENT
alternate interior angles are _____________.
a
3
d 4
e f
Angle 3 is congruent
to angle 4. They are
alternate interior
angles.
b
c
Use the AIA conjecture to
determine which angle is
congruent to angle c???
Answer: angle d
Alternate Exterior Angles Conjecture C-3c
(AEA Conjecture)
 If two parallel lines are cut by a transversal, then
alternate exterior angles are _____________.
CONGRUENT
A B
C D
EF
G H
According to the AEA
conjecture, list all congruent
angles.
Answer:
Angle A and Angle H
Angle B and Angle G
CONVERSE OF THE PARALLEL LINES CONJECTURE
C-4
 If two lines are cut by a transversal to form pairs of
congruent corresponding angles, congruent alternate
interior angles, or congruent alternate exterior
angles, then the lines are…………………………….
HOMEWORK
 Page 124; #1-6
 Page 131; #1-7, 9,10, 14-16