10.1 Points, Lines, Planes and Angles

Points

• A point is a location.

• It has no size or dimension.

• It is represented by a dot.

• We name a point using capital letters.

Point A

A

Lines

• A line is the shortest path connecting two points.

• It extends in both directions infinitely

• We name a line using any two points on the line.

Planes

• A plane is a flat surface with no thickness.

• It extends in all directions infinitely.

PPlane P

Parts of a line• A ray has a point at one end and extends

infinitely in the other direction.

• A line segment is the portion of a line connecting two points including the endpoints

Angles

• An angle is formed by two rays with a common endpoint called the vertex.

• The angle below can be named in the following ways: 1, B, ABC, CBA

A

BC

1

Angles continued• An angle can be thought of as the rotation

between two rays.

• The ray where the rotation begins is called the initial side.

• The ray where the rotation ends is called the terminal side

Initial side

Terminal side

Measuring angles• Angles are measured by the amount of

rotation from the initial side to the terminal side.

• One way to measure angles is in degrees

• One degree or 1° is 1/360 of a complete rotation.

• A complete rotation is 360°

• Angles are measured using protractors.

Angles and their degrees• An quarter rotation is 90°, a right angle.

• An acute angle is less than 90°

• A half rotation is 180°, a straight angle.

• An obtuse angle is between 90° and 180°

Right Acute Obtuse

Straight

Complementary and Supplementary

• Complementary angles are angles whose measures have a sum of 90°

• Supplementary angles are angles whose measures have a sum of 180°

• Find the supplement and complement of 25°

Example: Find the numbered angle

62 ° 1

54 ° 2

Example

• If 1 and 2 are supplementary and 1 is 66° more than 2, find the measure of each angle.

Vertical Angles• When two lines intersect, the angles

opposite one another are called vertical angles. Vertical angles have the same measure (i.e.are congruent).

• Find the numbered angles.

68°1

23

Parallel lines • When two parallel lines are intersected by a

line it is called a transversal.

1 2

3 4

5 67 8

*3 & 6 are alternate interior angles.

*1 & 8 are alternate exterior angles.

*1 & 5 are corresponding angles

Example

• Find the measure of the numbered angles

45

3 2

35 ° 7

6 1

HW: p. 497/5-32