© 2008 pearson addison-wesley. all rights reserved 9-1-1 chapter 1 section 9-1 points, lines,...

© 2008 Pearson Addison-Wesley. All rights reserved

9-1-1

Chapter 1

Section 9-1Points, Lines, Planes, and Angles


9-1-2

Points, Lines, Planes, and Angles

• The Geometry of Euclid

• Points, Lines, and Planes

• Angles


9-1-3

The Geometry of Euclid

A point has

A line has

A plane is


9-1-4

Points, Lines, and Planes

A

DE

l

A capital letter usually represents a point. A line may named by two capital letters representing points that lie on the line or by a single letter such as l. A plane may be named by three capital letters representing points that lie in the plane or by a letter of the Greek alphabet such as , , or .


9-1-5

Half-Line, Ray, and Line Segment

A point divides a line into two half-lines, one on each side of the point.

A __________ is a half-line including an initial point.

A _____________ includes two endpoints.


9-1-6

Half-Line, Ray, and Line Segment

Name Figure Symbol

Line AB or BA

Half-line AB

Half-line BA

Ray AB

Ray BA

Segment AB or segment BA


9-1-7

Parallel and Intersecting Lines

Parallel lines lie in the same plane and never meet.

Two distinct intersecting lines meet at a point.

Skew lines do not lie in the same plane and do not meet.


9-1-8

Parallel and Intersecting Planes

Parallel planes never meet.

Two distinct intersecting planes meet and form a straight line.

Parallel Intersecting


9-1-9

Angles

An angle is the union of two rays that have a common endpoint. An angle can be named with the letter marking its vertex, and also with three letters: - the first letter names a point on the side; the second names the vertex; the third names a point on the other side.

ABC,B


9-1-10

Angles

Angles are measured by the amount of rotation. 360° is the amount of rotation of a ray back onto itself.

45°90°

10°

150°360°


9-1-11

Angles

Angles are classified and named with reference to their degree measure.

Measure Name

Between 0° and 90°

90°

Greater than 90° but less than 180°

180°


9-1-12

Protractor

A tool called a protractor can be used to measure angles.


9-1-13

Intersecting Lines

When two lines intersect to form right angles they are called perpendicular.


9-1-14

Vertical Angles

In the figure below the pairare called vertical angles.are also vertical angles.

A

CB

D

E

and ABC DBE and DBA EBC

Vertical angles have equal measures.


9-1-15

Example: Finding Angle Measure

Find the measure of each marked angle below.

(3x + 10)° (5x – 10)°

Solution


9-1-16

Complementary and Supplementary Angles

If the sum of the measures of two acute angles is 90°, the angles are said to be _________________, and each is called the ________________ of the other. For example, 50° and 40° are complementary angles

If the sum of the measures of two angles is 180°, the angles are said to be _________________, and each is called the ____________ of the other. For example, 50° and 130° are supplementary angles


9-1-17



(2x + 45)° (x – 15)°

Solution


9-1-18

Angles Formed When Parallel Lines are Crossed by a Transversal

1 2

3 4

5 6

7 8

The 8 angles formed will be discussed on the next few slides.


9-1-19


1

5 4

8

(also 3 and 6)

(also 2 and 7)

Name


9-1-20


Interior angles on same side of transversal

Corresponding angles

Angle measures are equal.

Angle measures add to 180°.

46

2

6

(also 3 and 5)

(also 1 and 5, 3 and 7, 4 and 8)

Name


9-1-21



(x + 70)°(3x – 80)°

Solution

© 2008 pearson addison-wesley. all rights reserved 9-1-1 chapter 1 section 9-1 points, lines,...

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angles angles

planes angles

distinct intersecting

skew lines

right angles

straight line