Measuring Segments and Angles

During this lesson, you will use segmentpostulates to determine the lengths of segments.

A coordinate is a point’s

Segment Vocabularydistance and direction from 0 on a number line

Ex. Point A is Point B is

AB = _____units

-2 0 3A B

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

2 units left of 03 units right of 0

5

Ruler PostulateThe points on a line can be put into a one-to-one correspondence with the real numbers so that the distance between any two numbers _______________________________________________.

is the absolute value of their difference.

-2 0 3A B AB = │-2-3│= _____

AB = │-2-3│= _____

Ex.

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

segments.

Notation for congruent segments:

Congruent () segments are segmentswith the same length.

Use AB = CD (no bar on top) when referring to the lengths (or #’s).

Read: “segment AB is congruent to segment CD”

Read: “ measure of segment AB is equal to measure of segment CD”

Actual segments

A BC D

A BC D

2cm.2cm.

AB = CD

Lengths (or numbers)AB CD

mAB = mCD

A midpoint is a point that __________________________________.

divides a segment into two segments.

QR RS

Q SR

R is the midpoint of QS therefore:

m QR = m RSQR = RS

A

B

C

POSTULATE Segment Addition Postulate

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

AB + BC = AC

2x - 8 3x - 12D S

T

Substitute

Solve for x

DS + ST = DT2x - 8 + 3x - 12 = 60

5x - 20 = 605x = 80x = 16DS = 2x - 8 ST = 3x - 12

DS = 2(16) - 8DS = 24

ST = 36

Ex. #1 If DT = 60, find the value of x. Then find DS and ST.

Segment Addition Postulate

ST = 3(16) - 12

EX. #2 Comparing Segment Lengths

Compare AD and BF.

Compare BD and EG.

0 3 5 7 8-2-6

A B C D E F G

AD = 9 BF = 9 So, AD = BF

BD = 5 EG = 3 So, BD > EG

EX. #3 Using the Midpoint

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

RM

T

Def. of midpt.

5x + 9 8x - 36

RM = MTSubstitute5x + 9 = 8x - 36Solve for x 45 = 3x

15 = x

RM = 5x + 9RM = 5(15) + 9

RM = 84 = MT

RT = 84 + 84 = 168

C DA B

Final Checks for Understanding1. What is a postulate?2. Draw a sketch of three collinear

points. Label them. Then write the Segment Addition Postulate for the points.

3. Use the diagram. How can you determine BD if you know BC and CD?

Homework Assignment:

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