SEGMENT ADDITION

This stuff is AWESOME!

Can you see a shark?What about now?

Lesson 1-2: Segments and Rays 3

Between

Definition: X is between A and B if AX + XB = AB.

AX + XB = AB

Notice that this does not say X is in the middle of A and B; it is just somewhere between A and B. Therefore AX may not equal XB

Lesson 1-2: Segments and Rays 4

The Segment Addition Postulate

If C is between A and B, then AC + CB = AB.Postulate:

Example: If AC = x , CB = 2x and AB = 12, then, find x, AC and CB.

AC + CB = AB

x + 2x = 12

3x = 12

x = 4

2xx

12

x = 4AC = 4CB = 8

Step 1: Draw a figure

Step 2: Label fig. with given info.

Step 3: Write an equation

Step 4: Solve and find all the answers

Lesson 1-2: Segments and Rays 5

Congruent Segments

Definition:

If numbers are equal the objects are congruent.

AB: the segment AB ( an object )

AB: the distance from A to B ( a number )

Congruent segments can be marked with dashes.

Correct notation:

Incorrect notation:

Segments with equal lengths. (congruent symbol: )

Lesson 1-2: Segments and Rays 6

BisectTo cut into two equal parts.

FOR SEGMENTS: Any segment, line or plane that divides into two congruent parts, intersecting the segment at it’s midpoint.

Definition:

N is between L and P. LN = 14 and PN = 12. Find LP.

L PN

Q is between R and T. RT = 18 and QR = 10. Find QT.

R TQ

14 12

18

10

Find MN if N is between M and P, MN = 3x + 2,NP = 18, and MP = 5x.

M PN3x + 2 18

5x

3x + 2 + 18 = 5x 3x + 20 = 5x -3x -3x 20 = 2x 2 2 10 = x

MN = 3 (10 ) + 2MN = 32

YOU TRY!!

1)B is between A and C. Find the value of x and the measure of BC if: AB = 3, BC = 4x + 1, AC = 8.

3x + 2 8

5x

3x + 2 + 18 = 5x 3x + 20 = 5x -3x -3x 20 = 2x 2 2 10 = x

MN = 3 (10 ) + 2MN = 32

You Try!!!1. B is between A and C. Find the value of x and the measure of BC if: AB

= 3, BC = 4x + 1, AC = 8.

2. Y is between X and Z, find the value of x and the measure of XZ. XY = 24, YZ = 3x, XZ = 7x – 4.

3. If M is between L and N and LM = 2, MN = 4x + 6, LN = 32, then find x and MN.

4. If F is between E and G and EF = 26, FG = 5x, EG = 9x –6, find x and EG.