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Chapter 1Basics of Geometry

- By Carly Overleese, Karmen Spiker and Lindsey

Lewis

1.1

- Identify the pattern in the picture.
- What is the next figure?

You Try It Now

- What is the next three numbers.
- 15,30,45,60...

- What is the Pattern?
- 225,45,11.25,3.75

225,45,11.25,3.75 5 4 3 2

75,90,105

1.2

- Points, Lines, and Planes

1.2

- Line-
- Plane

1.2

- Line Segment
- Ray Initial Point
- Opposite rays

Now You Try

- Draw four noncollinear points.
- Label A,B,C,D.
- Draw a Segment from AB.
- Draw a line through BC.
- Through CD draw a ray.
- Draw a segment through AD.

B

C

A

D

1.2

- Collinear Points-
- Coplanar
- Points-

1.3

- Segments and Their Measures

1.3Postulate 1- The Ruler Postulate

- The points on a line can be matched one to one

with the real numbers. The real number that

corresponds to a point is the coordinate of the

point. - The Distance between points A and B, written as

AB, is the absolute value of the difference

between the coordinates of A and B. - AB is also called the length of AB.

A

B

1.3Postulate 2 Segment Addition Postulate

- If B is between A and C, then ABBCAC.
- If ABBCAC, then B is between A and C.

A

C

B

Distance Formula

- If A(x1,y1) and B(x2,y2) are points in a

coordinate plane, then the distance between A and

B is

AB (x2-x1) 2 (y2-y1)2

Using the Distance Formula

- Use the Distance Formula to find the lengths

between the two points. - A(-1,1) B(-4,3)
- Try and then we will check it..

ANSWER

AB (x2-x1) 2 (y2-y1)2

((-4)- (-1))2 (3-1) 2

(-3)2 22

94

13

DID YOU GET IT CORRECT?

Now your turn to try it

E

- In the picture of collinear points,
- AE20
- BD6
- ABBCCD

D

- Find Each Length
- BC
- AB
- AC
- AD

C

3

B

3

A

6

9

1.4

- Angles and Their Measures

Angle

Naming Angles

- What are the two names of the angle?

C

A

L ABC and L CBA

B

1.4Postulate 3 Protractor Postulate

- Consider a point A on one side of OB. The rays

of the form OA can be matched one to one with the

real numbers from 0 to 180. The measure of L AOB

is equal to the absolute value of the difference

between the real numbers for OA and OB.

A

B

O

1.4Postulate 4 Angle Addition Postulate

- If P is in the interior of L RST, then
- mLRSPmLPSTmLRST

R

mLRST

mLRSP

S

P

mLPST

T

Acute Angle

- An angle with a measure between 0 degrees and 90

degrees

Right Angle

- An angle with a measure of 90 degrees.

Obtuse Angle

- An angle with a measure between 90 degrees and

180 degrees.

Straight Angle

- An angle with a measure of 180 degrees.

Adjacent Angles

- Two angles with a common vertex and side, but no

common interior points.

Now your Turn

- Using the Angle Addition Postulate.
- What is mLDBC?

Answer30

A

60

D

B

C

1.5

- Segment and Angle Bisectors

Midpoint Formula

- If A(x1,y1) and B(x2,y2) are points in a

coordinate plane, then the midpoint of AB has

coordinates.

- (x1,y1)
- (x2,y2)

Your turn Applying Midpoint Formula

- Find the midpoint of AB.

- A(-2,3) and B(5,-2)

ANSWER 3, 1 2 2

1.6

- Angle Pair Relationships

Vertical Angles/ Linear Pair

- Consists of two angles whose sides form two pairs

of opposite rays.

Consists of two adjacent angles whose non-common

sides are opposite rays.

5

6

L1 and L3 are vertical angles. L2 and L4 are

vertical angles.

L5 and L6 are linear pairs

Finding the Angle Measure

- Find the Measurement of L1.

Answer 150

30

1

Answer 45

45

1

That concludes Chapter 1.Basics of Geometry.

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