1. Chapter 1: Tools of Geometry
Lesson 5: Measuring Segments

2. Definitions
Congruent- same shape and size (segments that have the same measure)

3. Distance between points
A. Find LM.
B. Find XZ.

4. Postulate 1-5 Ruler Postulate
The distance between points A and B, written as AB, is the absolute value of the difference of the coordinates of A and B.
AB = I a- b I
Use |Absolute Value|!!! A B
Since A is at -2 and B is at 4, we can say the distance from A to B or B to A is:
-2 – 4 = 6 or 4 – (-2) = 6

5. 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. 2x
4x + 6 C A B
AB = 2x BC = 4x + 6 AC = 60
Use the Segment Addition Postulate find the measure of AB and BC.

6. Step 1:
AB + BC = AC (Segment Addition) 2x + 4x + 6 = 60 6x + 6 = 60 6x = 54 x =9 AB = 2x = 2(9) = 18 BC =4x + 6 = 4(9) + 6 = 42
Step 2:
Step 3:
Step 4:

7. Use the diagram to find GH.
EXAMPLE 3
Find a length
Use the diagram to find GH.
SOLUTION
Use the Segment Addition Postulate to write an equation. Then solve the equation to find GH.
FG + GH = FH
Segment Addition Postulate.
21 + GH = 36
Substitute 36 for FH and 21 for FG. = 15 GH
Subtract 21 from each side.

8. Definitions
Midpoint- the point on a segment that divides the segment into two congruent segments
Segment bisector- any line, segment or plane that intersects a segment at its midpoint

9. Homework Pg