1. Section 1.3 Measuring Segments

2. Students will be able to: find and compare lengths of segments
Objective:
Students will be able to:
find and compare lengths of segments
1.3 Measuring Segments

3. coordinate distance congruent segments midpoint S=segment bisector
Vocabulary:
coordinate
distance
congruent segments
midpoint
S=segment bisector
1.3 Measuring Segments

4. This value is also AB, or the length between A and B.
The distance between points A and B is the absolute value of the difference of their coordinates,
or |a – b|.
This value is also AB, or the length between A and B.
1.3 Measuring Segments

5. Problem 1: What is ST? What is UV? What is SV?
1.3 Measuring Segments

6. Problem 1 Solution: What is ST? What is UV? What is SV?
8 – (-4) 
8 + 4 = 12
14 – 10 = 4
14 – (-4) 
1 + 4 = 18
1.3 Measuring Segments

7. 1.3 Measuring Segments

8. What algebraic expression represents EG?
Problem 2:
If EG = 59, what are EF and FG?
What algebraic expression represents EG?
What is the numeric value given for EG?
How should you check to make sure that the segment lengths are correct?
1.3 Measuring Segments

9. What algebraic expression represents EG?
Problem 2 Solution:
If EG = 59, what are EF and FG?
What algebraic expression represents EG?
What is the numeric value given for EG?
How should you check to make sure that the segment lengths are correct?
(8x -14) + (4x + 1 ) 
12x - 13 59
12x = 59 
12x = 72 
x = 6
EF: 8x - 14
FG: 4x + 1
8(6) - 14
4(6) + 1
8(6)  34
4(6) + 1  25
1.3 Measuring Segments

10. The symbol for congruent is ____________.
When numerical expressions have the same value, you say that they are equal (=).
Similarly, if two segments have the same length, then the segments are congruent segments.
The symbol for congruent is ____________.
1.3 Measuring Segments

11. This means if AB = CD, then . You can also say that if , then AB = CD.
1.3 Measuring Segments

12. Is Segment AB congruent to Segment DE?
Problem 3 Solution:
Are and congruent?
Is Segment AB congruent to Segment DE?
1.3 Measuring Segments

13. Problem 3: Are and congruent?
AC =| – 2 – 5 |
BD =| 3 – 10 |
=| – 7 |
=| – 7 |
= 7 units
= 7 units
Is Segment AB congruent to Segment DE?
YES. Since AC = BD.
1.3 Measuring Segments

14. That point, line, ray, or segment is called a segment bisector.
The midpoint of a segment is a point that divides the segment into two congruent segments.
A point, line, ray, or other segment that intersects a segment at its midpoint is said to bisect the segment.
That point, line, ray, or segment is called a segment bisector.
1.3 Measuring Segments

15. Problem 4: Q is the midpoint of . What are PQ, QR, and PR?
1.3 Measuring Segments

16. Problem 4 Solution: Q is the midpoint of . What are PQ, QR, and PR?
Midpoint = Halfway  Middle
6x – 7 = 5x + 1
PQ = 6x - 7
QR = 5x +1
PR = PR + QR
- 5x x
PQ = 6(8) - 7
QR = 5(8) +1
PR =
x – 7 = 1
PQ =
QR = 40 +1
PQ = 41
PR = 82
QR = 41
x = 8
1.3 Measuring Segments

17. Problem 4(b): U is the midpoint of . What are TU, UV, and TV?
1.3 Measuring Segments

18. Problem 4(b): U is the midpoint of . What are TU, UV, and TV?
Midpoint = Halfway  Middle
8x + 11 = 12x - 1
TU = 8x + 11
UV = 12x -1
TV = TU + UV
- 8x x
TU = 8(3) + 11
UV = 12(3) -1
TV =
11 = 4x - 1
TU =
UV =
TU = 35
TV = 70
UV = 35
12 = 4x
3 = x
1.3 Measuring Segments

19. Lesson Check
1.3 Measuring Segments

20. Lesson Check
1.3 Measuring Segments