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

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

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

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

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

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

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

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

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

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

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

Concept

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

Find Measurements by Adding or Subtracting Example 1

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. 16.8 mm B. 57.4 mm C. 67.2 mm D. 84 mm Example 1

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 – 3 + 3 = 45 + 3 Add 3 to each side. 12x = 48 Simplify. Example 2

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

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

Concept

Concept

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

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

Concept

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

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

Find Distance on a Coordinate Plane . Example 4

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

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

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

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 = 502 + 102 c2 = 2600 c ≈ 51 Example 5

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

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. 45.9 yards B. 50.7 yards C. 41.2 yards D. 31. 6 yards Example 5

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