1. Line Segments and Distance
LESSON 1–2
Line Segments and Distance

2. Five-Minute Check (over Lesson 1–1) TEKS Then/Now New Vocabulary
Key Concept: Betweenness of Points
Example 1: Finding Measurements by Adding or Subtracting
Example 2: Write and Solve Equations to Find Measurements
Key Concept: Congruent Segments
Key Concept: Distance Formula (on Number Line)
Example 3: Find Distance on a Number Line
Key Concept: Distance Formula (in Coordinate Plane)
Example 4: Find Distance on a Coordinate Plane
Example 5: Find Distance
Lesson Menu

3. Name three collinear points.
A. A, B, Q
B. B, Q, T
C. A, B, T
D. T, A, Q
5-Minute Check 1

4. What is another name for AB?
A. AA
B. AT
C. BQ
D. QB
5-Minute Check 2

5. Name a line in plane Z.
A. AT
B. AW
C. AQ
D. BQ
5-Minute Check 3

6. Name the intersection of planes Z and W.
A. BZ
B. AW
C. AB
D. BQ
5-Minute Check 4

7. How many lines are in plane Z?
B. 4
C. 6
D. infinitely many
5-Minute Check 5

8. Which of the following statements is always false?
A. The intersection of a line and a plane is a point.
B. There is only one plane perpendicular to a given plane.
C. Collinear points are also coplanar.
D. A plane contains an infinite number of points.
5-Minute Check 6

9. Mathematical Processes G.1(E), Also addresses G.1(B)
Targeted TEKS
G.2(B) Derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including
congruence of segments and parallelism or perpendicularity of pairs of lines.
G.5(B) Construct congruent segments, congruent angles, a
segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and straightedge. Also addresses G.5(C).
Mathematical Processes
G.1(E), Also addresses G.1(B)
TEKS

10. You identified points, lines, and planes.
Calculate with measures.
Find the distance between two points.
Then/Now

11. line segment distance irrational number betweenness of points between
congruent
rigid transformation
congruent segments
construction
Vocabulary

12. Concept

13. Find XZ. Assume that the figure is not drawn to scale.
Find Measurements by Adding or Subtracting
Find XZ. Assume that the figure is not drawn to scale.
XZ is the measure of XZ. Point Y is between X and Z. XZ can be found by adding XY and YZ.
___
Example 1

14. Find Measurements by Adding or Subtracting
Example 1

15. Find BD. Assume that the figure is not drawn to scale.
16.8 mm
50.4 mm
Find BD. Assume that the figure is not drawn to scale.
A mm
B mm
C mm
D. 84 mm
Example 1

16. Draw a figure to represent this situation.
Write and Solve Equations to Find Measurements
ALGEBRA Find the value of x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3.
Draw a figure to represent this situation.
ST + TU = SU Betweenness of points
7x + 5x – 3 = 45 Substitute known values.
7x + 5x – = Add 3 to each side.
12x = 48 Simplify.
Example 2

17. x = 4 Simplify. Now find ST. ST = 7x Given = 7(4) x = 4 = 28 Multiply.
Write and Solve Equations to Find Measurements
x = 4 Simplify.
Now find ST.
ST = 7x Given
= 7(4) x = 4
= 28 Multiply.
Answer: x = 4, ST = 28
Example 2

18. ALGEBRA Find the value of n and WX if W is between X and Y, WX = 6n – 10, XY = 17, and WY = 3n.
A. n = 3; WX = 8
B. n = 3; WX = 9
C. n = 9; WX = 27
D. n = 9; WX = 44
Example 2

19. Concept

20. Concept

21. Use the number line to find QR.
Find Distance on a Number Line
Use the number line to find QR.
The coordinates of Q and R are –6 and –3.
QR = | –6 – (–3) | Distance Formula
= | –3 | or 3 Simplify.
Answer: 3
Example 3

22. Use the number line to find AX.
C. –2
D. –8
Example 3

23. Concept

24. Find the distance between E(–4, 1) and F(3, –1).
Find Distance on a Coordinate Plane
Find the distance between E(–4, 1) and F(3, –1).
(x1, y1) = (–4, 1) and (x2, y2) = (3, –1)
Example 4

25. Find Distance on a Coordinate Plane
Check Graph the ordered pairs and check by using the Pythagorean Theorem.
Example 4

26. Find Distance on a Coordinate Plane.
Example 4

27. Find the distance between A(–3, 4) and M(1, 2).
Example 4

28. Analyze First draw a diagram to represent the situation.
Find Distance
Josh is standing at the 30-yard line, 15 yards from the sideline, when he throws the football. Johnny catches it on the other team’s 20-yard line, 5 yards from the same sideline. How far did Josh throw the ball?
Analyze First draw a diagram to represent the situation.
Example 5

29. Find Distance
Formulate Use the Distance Formula where (x1, y1) = (30, 15) and (x2, y2) = (80, 5).
Determine
Example 5

30. Josh threw the football approximately 51 yards.
Find Distance
Josh threw the football approximately 51 yards.
Justify Josh is 50 yards from the other team’s 20-yard line where Johnny is located, and he is 10 yards farther from the sideline than Johnny. Use the Pythagorean Theorem to justify the answer.
c2 = a2 + b2
c2 =
c2 = 2600
c ≈ 51
Example 5

31. Find Distance
Evaluate You are able to determine Josh’s and Johnny’s locations in terms of points on a coordinate plane and can use the Distance Formula to calculate the distance between them. The calculated distance seems reasonable.
Example 5

32. FOOTBALL Ben is standing at the 40-yard line, 20 yards from the sideline, when he throws the football. Eric catches it on the other team’s 30-yard line 10 yards from the same sideline. How far did Ben throw the ball?
A yards
B yards
C yards
D yards
Example 5

33. Line Segments and Distance
LESSON 1–2
Line Segments and Distance