1. 1.2 – Use Segments and Congruence
Geometry
Ms. Rinaldi

2. Postulate 1 – The Ruler Postulate
In Geometry, a rule that is accepted without proof is called a postulate or axiom.
Postulate 1 – The Ruler Postulate

3. EXAMPLE 1
Apply the Ruler Postulate
Measure the length of ST to the nearest tenth of a centimeter.
The length of ST is about 3.4 centimeters.
ANSWER

4. EXAMPLE 2
Apply the Ruler Postulate
Use a ruler to measure the length of the segment to the nearest inch. 1 8 a.
1 in. 5 8
ANSWER b.
1 in. 3 8
ANSWER

5. Definition
Between –

6. Postulate 2 – Segment Addition Postulate

7. EXAMPLE 3
Apply the the Segment Addition Postulate
Maps
The cities shown on the map lie approximately in a straight line. Use the given distances to find the distance from Lubbock, Texas, to St. Louis, Missouri.
SOLUTION
Because Tulsa, Oklahoma, lies between Lubbock and St. Louis, you can apply the Segment Addition Postulate.
LS = LT + TS = = 740
The distance from Lubbock to St. Louis is about 740 miles.
ANSWER

8. EXAMPLE 4
Find a length
In Exercises 3 and 4, use the diagram shown. a.
Use the Segment Addition Postulate to find XZ.
ANSWER 73
In the diagram, WY = 30. Can you use the Segment Addition Postulate to find the distance between points W and Z? Explain your reasoning. b.
No; W is not between X and Z.
ANSWER

9. Use the diagram to find GH.
EXAMPLE 5
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.

10. EXAMPLE 6
Find a length
Use the diagram to find WX.
107
ANSWER

11. Definition
Congruent Segments –

12. EXAMPLE 7
Compare segments for congruence
Plot J(– 3, 4), K(2, 4), L(1, 3), and M(1, – 2) in a coordinate plane. Then determine whether JK and LM are congruent.

13. EXAMPLE 8
Compare segments for congruence
Plot the points A(– 2, 4), B(3, 4), C(0, 2), and D(0, – 2) in a coordinate plane. Then determine whether AB and CD are congruent.

14. Homework
Pages 12 – 13 # 1, 6-14, 20, 21-23

15. A. Answer the following.
2. D, E & F are the three collinear points. If DE = FE and DE = 2x + 8, FE = 5x + 2, find x.
6. Given the figure below.
SOLUTION:
Write an equation for x using definition of congruent segments, then solve.
DE = FE ( GIVEN)
2x + 8 = 5x + 2
8 – 2 = 5x – 2x
6 = 3x
2 = x
D E F
2x x +2