Lesson 9.2 Angle Relationships and Parallel Lines.

Anglesthat measure less than 90.

Angles that measure more than 90and less than 180.

Anglesthat measure exactly 90.

Types of Angles

Acute -

Right -

Obtuse -

Adjacent Angles

• Share a vertex and a side but no points in the interiors.

A

X

B

C

<AXB and <BXC are adjacent

angles

<AXC and <BXC are not adjacent angles

Why?

Complementary Angles

ab

- Angles whosesum is 90 .

m a m b 90

x y

m x m y 90

Complementary angles do nothave to be adjacent.

Supplementary Angles

kt

- Angles whosesum is 180 .

m k m t 180

b c

m b m c 180

Supplementary angles do nothave to be adjacent.

Congruent Angles

• Angles that have the same measurement• Notation:

1 3

1 3m m

Vertical Angles - Opposite angles that are formed by intersecting lines.

Opposite angles (vertical angles) are ALWAYS congruent.

b

a

ba

Identifying Corresponding Angles Transversal -A line that intersects

two other lines.

Identifying Corresponding Angles CorrespondingAngles

- Two angles that are formed by two lines and a transversal and occupy corresponding positions.

A B

C D

1 23 4

5 67 8

If the two lines are parallel, then the corresponding angles are congruent.

Corresponding Angles1 52 63 74 8

Identifying Alternate Interior Angles Alternate Interior Angles:-interior of a pair of lines on opposite

sides of the transversal.A B

C D

1 23 4

5 67 8

If the two lines are parallel, then the alternate interior angles are congruent.

Corresponding Angles3 64 5

(4n 30)

Find the value of n.

(n 10) (2n 30)

n

1) 2)

n (2n 30) 90 3n 30 90

30 30 3n 603 3n 20

(4n 30) (n 10) 180 5n 20 180

20 20 5n 1605 5n 32

Homework

• Page 452 -453 (1-11 all and 13)• Draw figures in the homework