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Measuring Segments and Angles

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Measuring Segments and Angles

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Measuring Segments and Angles

During this lesson, you will use segment

postulates to determine the lengths of

segments.

A

B

3

0

-2

Segment Vocabulary

distance and direction from 0

on a number line

A coordinate is a point’s

Ex. Point A is

Point B is

AB = _____units

2 units left of 0

3 units right of 0

5

Read: “the measure of line segment AB = 5”

A

B

3

0

-2

is the absolute value of their difference.

Ex.

AB = │-2-3│= _____

AB = │-2-3│= _____

Use AB CD (bar on top) when referring to the actual segments.

Congruent () segments are segments

with the same length.

Notation for congruent segments:

Read: “segment AB is congruent to segment CD”

Use AB = CD (no bar on top) when

referring to the lengths (or #’s).

Read: “ measure of segment AB is equal to

measure of segment CD”

2cm.

2cm.

AB CD

A

C

A

B

D

B

C

D

Actual segments

Lengths (or numbers)

AB = CD

mAB = mCD

Q

R

S

QR RS

m QR = m RS

R is the midpoint of QS therefore:

A midpoint is a point that __________________________________.

divides

a segment into two segments.

QR = RS

C

B

A

POSTULATE

Segment Addition Postulate

If three points A, B and C are collinear and B is between A and C, then

AB + BC = AC

Ex. #1 If DT = 60, find the value of x.

Then find DS and ST.

3x - 12

2x - 8

T

D

S

DS + ST = DT

Segment Addition Postulate

Substitute

2x - 8 + 3x - 12 = 60

Solve for x

5x - 20 = 60

5x = 80

DS= 2x - 8

x = 16

ST= 3x - 12

DS = 2(16) - 8

ST = 3(16) - 12

ST = 36

DS = 24

A

B

C

D

E

F

G

-6

-2

0

5

3

8

7

EX. #2 Comparing Segment Lengths

Compare AD and BF.

9

9

So, AD = BF

AD =

BF =

Compare BD and EG.

5

3

BD =

So, BD > EG

EG =

EX. #3 Using the Midpoint

8x - 36

5x + 9

T

R

M

M is the midpoint of RT. Find RM, MT and RT.

RM = MT

Def. of midpt.

5x + 9 = 8x - 36

Substitute

RM = 5x + 9

45 = 3x

Solve for x

RM = 5(15) + 9

15 = x

RM = 84 = MT

RT = 84 + 84 = 168

- What is a postulate?
- Draw a sketch of three collinear points. Label them. Then write the Segment Addition Postulate for the points.
- Use the diagram. How can you determine BD if you know BC and CD?

C D

A B

Pages 29-33, text: #1-15, 29-32, 42-46, 71-72