1. Lesson 2.5 Angle Relationships
Geometry Chapter 2
Lesson 2.5 Angle Relationships

2. Linear Pair Conjecture C-1
If two angles form a linear pair, then
the measure of the angles add up to 180 degrees. .

3. Vertical Angles Conjecture C-2
If two angles are vertical angles, then
they have equal measures (are congruent). 2
Measure of angle 1 equals the measure of angle ______. While the Measure of angle 2 equals the measure of angle ______. 3 1 4

4. Putting C-1 and C-2 Together
Example Problems: Solve for the missing variables.
Solution:
x = 180 (C-1)
x = 50
**Use C-2 to solve for y and z. x z y
Solution:
48 + a + 46 = 180 (Conjecture???)
a + 94 = 180
a = 86
**Use C-2 to solve for b,c,and d. a b c d

5. LESSON 2.6 SPECIAL ANGLES ON PARALLEL LINES
CHAPTER 2
LESSON 2.6
SPECIAL ANGLES ON PARALLEL LINES

6. PARALLEL LINES CONJECTURE C-3
If two parallel lines are cut by a transversal, then corresponding angles are…
alternate interior angles are…
and alternate exterior angles are…
CONGRUENT,
CONGRUENT,
CONGRUENT.
KEY: Lines must be proven parallel.

7. 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 They are corresponding angles.
52 degrees
Therefore, if angle 1 is 52 degrees, then angle 2 is __________.

8. Alternate Interior Angles Conjecture C-3b (AIA Conjecture)
If two parallel lines are cut by a transversal, then alternate interior angles are _____________.
CONGRUENT a b 3 c 4 d e f
Use the AIA conjecture to determine which angle is congruent to angle c???
Angle 3 is congruent to angle 4. They are alternate interior angles.
Answer: angle d

9. Alternate Exterior Angles Conjecture C-3c (AEA Conjecture)
If two parallel lines are cut by a transversal, then alternate exterior angles are _____________.
CONGRUENT
According to the AEA conjecture, list all congruent angles. A B C D E F G H
Answer:
Angle A and Angle H
Angle B and Angle G

10. 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…………………………….
PARALLEL

11. HOMEWORK
Page 124; #1-6
Page 131; #1-7, 9,10, 14-16