1.4 Measuring Segments and Angles

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1.4 Measuring Segments and Angles. Chapter 1 Tools of Geometry. Postulate 1-5 Ruler Postulate The distance between any two points is the absolute value of the difference of the corresponding numbers (on a number line or ruler) Congruent Segments : two segments with the same length.

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## 1.4 Measuring Segments and Angles

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### 1.4 Measuring Segments and Angles

Chapter 1 Tools of Geometry

Postulate 1-5 Ruler Postulate

The distance between any two points is the absolute value of the difference of the corresponding numbers (on a number line or ruler)

Congruent Segments: two segments with the same length

Comparing Segment Lengths
• Look in book for Example 1, pg 26
Postulate 1-6 Segment Addition Postulate

If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC

C

B

A

Using the Segment Addition Postulate

If DT = 60, find the value of x. Then find DS and ST.

2x - 8

3x - 12

D

S

T

Using the Segment Addition Postulate

If EG = 100, find the value of x. Then find EF and FG.

4x - 20

2x + 30

E

F

G

A

B

C

B is the midpoint, so AB = BC

Finding Lengths

C is the midpoint of AB. Find AC, CB, and AB.

3x – 4

2x + 1

A

C

B

27

X

Z

Y

Z is the midpoint of XY, and XY = 27. Find XZ.

Angle: formed by two rays with the same endpoint

The endpoint is called the vertex

Can be named by the vertex, by three letters with the vertex in the center, or by a number

A

<ABC

<CBA

<B

<1

B

1

C

*Look at example 4 in the book, pg 27

Postulate 1-7 Protractor Postulate

You can use a protractor to measure an angle.

*Look in book on page 28

Acute angle

< 90°

Right Angle

= 90°

Obtuse Angle

> 90° but < 180°

(90° < x < 180°)

*Example 5 on pg 28

Straight Angle

= 180°

Postulate 1-8 Angle Addition Postulate

If point B lies in the interior of <AOC, then m<AOB + m<BOC = m<AOC

If <AOC is a straight angle, then m<AOB + m<BOC = 180

A

B

O

C

B

A

O

C

Using Angle Addition Postulate

What is m<TSW if m<RST = 50 and m<RSW = 125?

T

W

x

50

R

S

Using The Angle Addition Postulate

If m<DEG = 145, find m<GEF.

G

145

x

D

E

F

Congruent Angles: Angles with the same measure

Homework

Pg 29 1-28