Section 3.1 Lines and Angles

Section 3.1 Lines and Angles

Perpendicular Lines• Intersecting lines that form right angles

• Symbol

T

XS SR

Parallel Lines• Two lines that are coplanar and do not

intersect

• Symbol: II

T

XY II UZ

Skew Lines• Lines do not intersect and are not coplanar

T

Example

• Is XY parallel or skew to RV?

T

XY II RV

Parallel planes• Two planes that do not intersect

T

Parallel Postulate

• If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.

Perpendicular Postulate

• If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.

Theorem 3.1

• If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular

• Ex 1

A B C

D

m<ABD = m<DBC and a linear pair, BD AC

Theorem 3.2

• If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.

• Ex. 2

H

F

G

J

<FGJ is complementary to <JGH

Examples: Solve for x

Ex 3.

60°x

ANSWER: 60 + x = 90

-60 -60

x = 30

Example 4

x55°

ANSWER: x + 55 = 90

-55 -55

x = 35

Example 5

27°

(2x-9)°

ANSWER: 2x – 9 + 27 = 90

2x +18 = 90

2x = 72

x = 36

Theorem 3.3

• If 2 lines are perpendicular, then they intersect to form four right angles.

m

l

Complete Try it! Problems

#1-8

Transversal• A line that intersects two or more coplanar

lines at different points.

transversal

Vertical Angles

• Formed by the intersection of two pairs of opposite rays

1 2

3 4

5 6

7 8

Linear Pair

• Adjacent angles that are supplementary

1 2

3 4

5 6

7 8

Corresponding Angles

• Occupy corresponding positions.

1 2

3 4

5 6

7 8

Alternate Exterior Angles

• Lie outside the 2 lines on opposite sides of the transversal.

1 2

3 4

5 6

7 8

Alternate Interior Angles• Lie between the 2 lines on opposite sides

of the transversal.

1 2

3 4

5 6

7 8

Consecutive Interior Angles(Same side interior angles)

• Lie between the 2 lines on the same side of the transversal.

1 2

3 4

5 6

7 8

Angle Relationships: Name a pair of angles

• Corresponding– Ex. 1 & 5

• Alternate Exterior – Ex. 2 & 7

• Alternate Interior– Ex. 4 & 5

• Consecutive Interior– Ex. 3 & 5

1 23 4

5 6

7 8