PRE-ALGEBRA

Find ALL of the missing angle measures.

40°

120°

120°60°

60°

40°

60°60° 180-(40+60) = 80°

80°

80°

80°

100°

100°

Classifying Polygons (9-2)

PRE-ALGEBRA

Angle Relationships and Parallel Lines (9-2)

What are congruent, adjacent and vertical angles?

Congruent angles are two or more angles that are equal in measure. The symbol is used to indicate two angles are congruent.

Adjacent angles are two angles that are side by side and share a common vertex and ray in the middle.

Vertical angles are two angles that are opposite of each other and formed when two lines intersect. Vertical angles are always congruent, or equal, to one another.

Example: In the figure below, MRN and NRQ are adjacent angles. They share vertex R and RN. NRQ.

Example: 1 2

Example: In the figure below, MRP and NRQ are vertical angles, so MRP NRQ.

PRE-ALGEBRA

Angle Relationships and Parallel Lines (9-2)

What are complementary and supplementary angles?

Complementary angles are two angles whose measures have a sum of 90 (together, they make a right angles).

Supplementary angles are two angles whose measures have a sum of 180 (together, they make a straight line).

Example: In the figure below, LMN and NMP are complementary angles, because 65 + 25 = 90.

Example: In the figure below, GHK and KHJ are supplementary angles, because 65 + 115 = 180.

P

N

M

L

25°

65°

J

K

H115°

65°G

PRE-ALGEBRA

Find the measure of 3 if m 4 = 110°.

Replace m 4 with 110°.m 3 + 110° = 180°

Solve for m 3.m 3 + 110° – 110° = 180° – 110°

m 3 = 70°

3 and 4 are supplementary.m 3 + m 4 = 180°

LESSON 9-2

Additional Examples

Angle Relationships and Parallel Lines

PRE-ALGEBRA

Angle Relationships and Parallel Lines (9-2)

What is a transversal?

Transversal – a line, line segment or ray that intersects two or more parallel or nonparallel lines at different points.

Corresponding Angles - two angles which are on the same sides of the transversal and the lines cut by the transversal (in other words, they’re in corresponding, or matching, positions).

Example: In the figures below, t is a transversal for l and m, and r is a transversal for b and c.

Example: In the two figures above, 1 and 5, 4 and 8, 2 and 6, and 3 and 7 are corresponding angles.

What are corresponding angles?

PRE-ALGEBRA

Angle Relationships and Parallel Lines (9-2)

What are alternating interior angles?

Alternating interior angles are angles that lie between two lines but on opposite sides of the transversal. NOTE: Alternating interior angles of two parallel lines are congruent.

What are alternating exterior angles?

Example: In the figure below, 4 and 6 and 3 and 5 are alternating interior angles, so 4 6 and 3 5

Alternating exterior angles are angles that lie outside two lines but on opposite sides of the transversal. NOTE: Alternating exterior angles of two parallel lines are congruent.

Example: In the figure below, 1 and 7 and 2 and 8 are alternating exterior angles, so 1 7 and 2 8

PRE-ALGEBRA

1 3, 2 4, 5 7, 6 8

2 7, 6 3

In the diagram, p || q. Identify each of the following.

a. congruent corresponding angles

b. congruent alternate interior angles

LESSON 9-2

Additional Examples

Angle Relationships and Parallel Lines

PRE-ALGEBRA

s t

c

d

1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

s || t and c || d.

Name all the angles that are congruent to 1. Give a reason for each answer.

3 1 corresponding angles

6 1 vertical angles

8 1 alternate exterior angles

9 1 corresponding angles

1 11 corresponding angles

14 1 alternate exterior angles

1 16 alternate exterior angles

Angle Relationships and Parallel Lines (9-2) Quiz