Do First

Complementary angles add up to 90º.

60º

30º40º

50º

Adjacent and Complementary Angles

Complementary Anglesbut not Adjacent

Supplementary Anglessum to 180°

30° 150°

2. Angle Relationships

2. Angle Relationships

Conjecture 2: Vertical Angles Conjecture

If two angles form vertical angles they are congruent.

Conjecture 3: Linear Pair Conjecture

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

2. Angle Relationships

Vertical Anglesare opposite one another.

Vertical angles are congruent.

100°

100°

Lines l and m are parallel.l||m

120°

l

m

120°

120°

120°

Note the 4 angles that measure 120°.

nLine n is a transversal.

Lines l and m are parallel.l||m

60°

l

m

60°

60°

60°

There are many pairs of angles that are supplementary.

There are 4 pairs of angles that are vertical.

120°

120°

120°

120°

nLine n is a transversal.

Conjecture 4: Triangle Sum Conjecture

The sum of the angles of a triangle is 180°.

2. Angle Relationships

5. Angle Relationships

Conjecture 5: Parallel Line Conjecture

If two parallel lines are cut by a transversal then:

alternate interior angles are congruent,alternate exterior angles are congruent, andcorresponding angles are congruent.

If two lines are intersected by a transversal and any of the angle pairs shown below are congruent, then the lines are parallel. This fact is used in the construction of parallel lines.

5. Angle Relationships

1 2

3 4

5 6

7 8

How many angles are there?

Corresponding angles.

Alternate interior angles

Alternate exterior angles

2 & 64 & 5

1 & 8

4 & 8 3 & 7 1 & 53 & 6

2 & 7

8

5. Angle Relationships

Conjecture 5: Parallel Line Conjecture

If two parallel lines are cut by a transversal then:

alternate interior angles are congruent,alternate exterior angles are congruent, andcorresponding angles are congruent.

1) Find the missing angle.

36°

?°

1) Find the missing angle.

36°

?°

90 ° – 36 = 54°

2) Find the missing angle.

64°

?°

2) Find the missing angle.

64°

?°

90 ° – 64° = 26°

5) Find the missing angle.

?° 168°

5) Find the missing angle.

?° 168°

180° – 168° = 12°

6) Find the missing angle.

58° ?°

6) Find the missing angle.

58° ?°

180° – 58° = 122°

7) Solve for x.

4x 5x

4x + 5x = 180

9x = 180

x = 20

8) Solve for x.

2x + 10 3x + 20

9) Lines l and m are parallel.l||m

Find the missing angles.

42°

l

m

b°

d°

f°

a °

c°

e°

g°

9) Lines l and m are parallel.l||m

Find the missing angles.

42°

l

m

42°

42°

42°

138°

138°

138°

138°

10) Lines l and m are parallel.l||m

Find the missing angles.

81°

l

m

b°

d°

f°

a °

c°

e°

g°

10) Lines l and m are parallel.l||m

Find the missing angles.

81°

l

m

81°

81°

81°

99°

99°

99°

99°

11) Find the missing angles.

70 °b°

70 °

d ° 65 °

Hint: The 3 angles in a triangle sum to 180°.

11) Find the missing angles.

70 °40°

70 °

75 ° 65 °

Hint: The 3 angles in a triangle sum to 180°.

12) Find the missing angles.

45 °b°

50 °

d ° 75 °

Hint: The 3 angles in a triangle sum to 180°.

12) Find the missing angles.

45 °85°

50 °

20° 75 °

Hint: The 3 angles in a triangle sum to 180°.

In the figure a || b.

13. Name the angles congruent to 3.

14. Name all the angles supplementary to 6.

15. If m1 = 105° what is m3?

16. If m5 = 120° what is m2?

1, 5, 7

1, 3, 5, 7

105°

60°