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Splash Screen. Five-Minute Check (over Lesson 3–5) CCSS Then/Now New Vocabulary Key Concept: Distance Between a Point and a Line Postulate 3.6: Perpendicular Postulate Example 1: Real-World Example: Construct Distance From Point to a Line

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 3–5) CCSS Then/Now New Vocabulary Key Concept: Distance Between a Point and a Line Postulate 3.6: Perpendicular Postulate Example 1: Real-World Example: Construct Distance From Point to a Line Example 2: Distance from a Point to a Line on Coordinate Plane Key Concept: Distance Between Parallel Lines Theorem 3.9: Two Line Equidistant from a Third Example 3: Distance Between Parallel Lines Lesson Menu

  3. Please read the following and consider yourself in it. I am capable of learning. I can accomplish mathematical tasks. I am ultimately responsible for my learning. An Affirmation

  4. Important Information What: The Benchmark will be the MIDTERM. When: B-Day 3/8 and 3/10 A-Day 3/7 Why: If not you would have had 3 consecutive tests- Benchmark, Midterm, and Mock EOC! Taking away from preparation as well as instructional time. Material Covered: Any material addressed since 1/4/17. See the Website for the Study Guides.

  5. Standards MGSE9-12.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. (Focus on quadrilaterals, right triangles, and circles.) MGSE9-12.G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). MGSE9-12.G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. MGSE9-12.G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

  6. ___ ___ A.AB || CD B.FG || HI C.CD || FG D. none __ ___ ___ ___ Given 9  13, which segments are parallel? 5-Minute Check 1

  7. ___ ___ A.AB || CD B.FG || HI C.CD || FG D. none __ ___ ___ ___ Given 9  13, which segments are parallel? 5-Minute Check 1

  8. ___ ___ A.AB || CD B.CD || FG C.FG || HI D. none ___ ___ __ ___ Given 2  5, which segments are parallel? A.AB || CD B.CD || FG C.FG || HI D. none 5-Minute Check 2

  9. ___ ___ A.AB || CD B.CD || FG C.FG || HI D. none ___ ___ __ ___ Given 2  5, which segments are parallel? A.AB || CD B.CD || FG C.FG || HI D. none 5-Minute Check 2

  10. ___ ___ If m2 + m4 = 180, then AB || CD. What postulate supports this? A. If consecutive interior s are supplementary, lines are ||. B. If alternate interior s are , lines are ||. C. If corresponding s are , lines are ||. D. If 2 lines cut by a transversal so that corresponding s are , then the lines are ||. 5-Minute Check 3

  11. ___ ___ If m2 + m4 = 180, then AB || CD. What postulate supports this? A. If consecutive interior s are supplementary, lines are ||. B. If alternate interior s are , lines are ||. C. If corresponding s are , lines are ||. D. If 2 lines cut by a transversal so that corresponding s are , then the lines are ||. 5-Minute Check 3

  12. ___ __ If 5  14, then CD || HI. What postulate supports this? A. If corresponding s are , lines are ||. B. If 2 lines are to the same line, they are ||. C. If alternate interior s are , lines are ||. D. If consecutive interior s are supplementary, lines are ||. ┴ 5-Minute Check 4

  13. ___ __ If 5  14, then CD || HI. What postulate supports this? A. If corresponding s are , lines are ||. B. If 2 lines are to the same line, they are ||. C. If alternate interior s are , lines are ||. D. If consecutive interior s are supplementary, lines are ||. ┴ 5-Minute Check 4

  14. ___ __ Find x so that AB || HI if m1 = 4x + 6 and m14 = 7x – 27. . A. 6.27 B. 11 C. 14.45 D. 18 5-Minute Check 5

  15. ___ __ Find x so that AB || HI if m1 = 4x + 6 and m14 = 7x – 27. . A. 6.27 B. 11 C. 14.45 D. 18 5-Minute Check 5

  16. Two lines in the same plane do not intersect. Which term best describes the relationship between the lines? A. parallel B. perpendicular C. skew D. transversal 5-Minute Check 6

  17. Two lines in the same plane do not intersect. Which term best describes the relationship between the lines? A. parallel B. perpendicular C. skew D. transversal 5-Minute Check 6

  18. Content Standards G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Mathematical Practices 2 Reason abstractly and quantitatively. 4 Model with mathematics. CCSS

  19. equidistant Vocabulary

  20. Concept

  21. CONSTRUCTION A certain rooftruss is designed so that the center post extends from the peak of the roof (point A) to the main beam. Construct and name the segment whose length represents the shortest length of wood that will be needed to connect the peak of the roof to the main beam. The distance from a line to a point not on the line is the length of the segment perpendicular to the line from the point. Locate points R and S on the main beam equidistant from point A. Construct Distance From Point to a Line Example 1

  22. Locate a second point not on the beam equidistant from Rand S. Construct AB so that AB is perpendicular to the beam. Construct Distance From Point to a Line Answer: Example 1

  23. Locate a second point not on the beam equidistant from Rand S. Construct AB so that AB is perpendicular to the beam. ___ Answer:The measure of AB represents the shortest length of wood needed to connect the peak of the roof to the main beam. Construct Distance From Point to a Line Example 1

  24. KITES Which segment represents the shortest distance from point A to DB? A.AD B.AB C.CX D.AX Example 1

  25. KITES Which segment represents the shortest distance from point A to DB? A.AD B.AB C.CX D.AX Example 1

  26. COORDINATE GEOMETRY Line s contains points at (0, 0) and (–5, 5). Find the distance between line s and point V(1, 5). (–5,5) V(1,5) (0,0) Distance from a Point to a Line on Coordinate Plane Step 1 Find the slope of line s. Begin by finding the slope of the line through points (0, 0) and (–5, 5). Example 2

  27. Distance from a Point to a Line on Coordinate Plane Then write the equation of this line by using the point (0, 0) on the line. Slope-intercept form m = –1, (x1, y1) = (0, 0) Simplify. The equation of line s is y = –x. Example 2

  28. Distance from a Point to a Line on Coordinate Plane Step 2 Write an equation of the line t perpendicular to line s through V(1, 5). Since the slope of line s is –1, the slope of line t is 1. Write the equation for line t through V(1, 5) with a slope of 1. Slope-intercept form m = 1, (x1, y1) = (1, 5) Simplify. Subtract 1 from each side. The equation of line t is y = x + 4. Example 2

  29. Distance from a Point to a Line on Coordinate Plane Step 3 Solve the system of equations to determine the point of intersection. line s: y = –x line t: (+) y =x + 4 2y = 4 Add the two equations. y = 2 Divide each side by 2. Solve for x. 2 = –x Substitute 2 for y in the first equation. –2 = x Divide each side by –1. The point of intersection is (–2, 2). Let this point be Z. Example 2

  30. Distance from a Point to a Line on Coordinate Plane Step 4 Use the Distance Formula to determine the distance between Z(–2, 2) and V(1, 5). Distance formula Substitution Simplify. Answer: Example 2

  31. Answer:The distance between the point and the line is or about 4.24 units. Distance from a Point to a Line on Coordinate Plane Step 4 Use the Distance Formula to determine the distance between Z(–2, 2) and V(1, 5). Distance formula Substitution Simplify. Example 2

  32. (2,4) B(3,1) (–4,2) A. B. C. D. COORDINATE GEOMETRY Line n contains points (2, 4) and (–4, –2). Find the distance between line n and point B(3, 1). Example 2

  33. (2,4) B(3,1) (–4,2) A. B. C. D. COORDINATE GEOMETRY Line n contains points (2, 4) and (–4, –2). Find the distance between line n and point B(3, 1). Example 2

  34. Concept

  35. Concept

  36. Find the distance between the parallel lines a and b whose equations are y = 2x + 3 and y = 2x – 1, respectively. Distance Between Parallel Lines a b You will need to solve a system of equations to find the endpoints of a segment that is perpendicular to both a and b. From their equations,we know that the slope of line a and line b is 2. Sketch line p through they-intercept of line b, (0, –1),perpendicular to lines a and b. p Example 3

  37. Write an equation for line p. The slope of p is theopposite reciprocal of Point-slope form Simplify. Subtract 1 from each side. Distance Between Parallel Lines Step 1 Use the y-intercept of line b, (0, –1), as one of the endpoints of the perpendicular segment. Example 3

  38. Substitute 2x + 3 for y in the second equation. Group like terms on each side. Distance Between Parallel Lines Step 2 Use a system of equations to determine the point of intersection of the lines a and p. Example 3

  39. Simplify on each side. Multiply each side by . Substitute for x in theequation for p. Distance Between Parallel Lines Example 3

  40. Simplify. The point of intersection is or (–1.6, –0.2). Distance Between Parallel Lines Example 3

  41. Distance Formula x2 = –1.6, x1 = 0,y2 = –0.2, y1 = –1 Distance Between Parallel Lines Step 3 Use the Distance Formula to determine the distance between (0, –1) and (–1.6, –0.2). Answer: Example 3

  42. Distance Formula x2 = –1.6, x1 = 0,y2 = –0.2, y1 = –1 Distance Between Parallel Lines Step 3 Use the Distance Formula to determine the distance between (0, –1) and (–1.6, –0.2). Answer:The distance between the lines is about 1.79 units. Example 3

  43. Find the distance between the parallel lines a and b whose equations are and ,respectively. A. 2.13 units B. 3.16 units C. 2.85 units D. 3 units Example 3

  44. Find the distance between the parallel lines a and b whose equations are and ,respectively. A. 2.13 units B. 3.16 units C. 2.85 units D. 3 units Example 3

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