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Lesson 1 Menu

Find the geometric mean between 8 and 15. State the exact answer. Determine whether the numbers 6, 9, and 12 are the sides of a right triangle. In Δ ABC , if m  C = 90, AB = x , AC = y , and CB = z , then find cos A .

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Lesson 1 Menu

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  1. Find the geometric mean between 8 and 15. State the exact answer. • Determine whether the numbers 6, 9, and 12 are the sides of a right triangle. • In ΔABC, if mC = 90, AB = x, AC = y, and CB = z, then find cos A. • In ΔABC, if mC = 90, AB = x, AC = y, and CB = z, then find sin A. • In ΔABC, if mC = 90, AB = x, AC = y, and CB = z, then find tan B. Lesson 1 Menu

  2. Draw reflected images. • Recognize and draw lines of symmetry and points of symmetry. • reflection • line of reflection • isometry • line of symmetry • point of symmetry Lesson 1 MI/Vocab

  3. Step 2Locate W', X', Y', and Z' so that line p is the perpendicular bisector of Points W', X', Y', and Z' are the respective images of W, X, Y, and Z. Reflecting a Figure in a Line Draw the reflected image of quadrilateral WXYZ in line p. Step 1Draw segments perpendicular to line p from each point W, X, Y, and Z. Lesson 1 Ex1

  4. Reflecting a Figure in a Line Step 3Connect vertices W', X', Y', and Z'. Answer:Since points W', X', Y', and Z' are the images of points W, X, Y, and Z under reflection in line p, then quadrilateral W'X'Y'Z' is the reflection of quadrilateral WXYZ in line p. Lesson 1 Ex1

  5. A. B. C. D. Draw the reflected image of quadrilateral ABCD in line n. • A • B • C • D Lesson 1 CYP1

  6. Reflection on a Coordinate Plane A. COORDINATE GEOMETRY Quadrilateral ABCD has vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3). Graph ABCD and its image under reflection in the x-axis. Compare the coordinates of each vertex with the coordinates of its image. Use the vertical grid lines to find the corresponding point for each vertex so that the x-axis is equidistant from each vertex and its image. A(1, 1) A' (1, –1) B(3, 2) B' (3, –2) C(4, –1) C' (4, 1) D(2, –3) D' (2, 3) Lesson 1 Ex2

  7. Reflection on a Coordinate Plane Plot the reflected vertices and connect to form the image A'B'C'D'. Answer: The x-coordinates stay the same, but the y-coordinates are opposite. That is, (a, b)  (a, –b). Lesson 1 Ex2

  8. Reflection on a Coordinate Plane B. COORDINATE GEOMETRY Quadrilateral ABCD has vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3). Graph ABCD and its image under reflection in the origin. Compare the coordinates of each vertex with the coordinates of its image. Use the horizontal grid lines to find the corresponding point for each vertex so that the y-axis is equidistant from each vertex and its image. A(1, 1) A' (–1, –1) B(3, 2) B' (–3, –2) C(4, –1) C' (–4, 1) D(2, –3) D' (–2, 3) Lesson 1 Ex2

  9. Reflection on a Coordinate Plane Plot the reflected vertices and connect to form the image A'B'C'D'. The x-coordinates and y-coordinates are opposite. That is, (a, b)  (–a, –b). Answer: (a, b)  (–a, –b) Lesson 1 Ex2

  10. Reflection on a Coordinate Plane C. COORDINATE GEOMETRY Quadrilateral ABCD has vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3). Graph ABCD and its image under reflection in the line y = x. Compare the coordinates of each vertex with the coordinates of its image. Lesson 1 Ex2

  11. Since point A is on the line y = x, A' is in the same location as A. For point B, locate its image on the other side of y = x so that this line is perpendicular bisector of The slope of y = x is 1, so the slope of must be –1. From B to the line y = x, move up unit and left unit. From the line y = x, move up unit and left unit to B'. Repeat for point C and D. Reflection on a Coordinate Plane Lesson 1 Ex2

  12. Reflection on a Coordinate Plane A(1, 1) A' (1, 1) B(3, 2) B' (2, 3) C(4, –1) C' (–1, 4) D(2, –3) D' (–3, 2) Plot the reflected verticesand connect to form the image A'B'C'D'. Answer: The x-coordinates becomes the y-coordinate and the y-coordinate becomes the y-coordinate. That is, (a, b)  (b, a). Lesson 1 Ex2

  13. A. COORDINATE GEOMETRY Quadrilateral LMNP has vertices L(–1, 1), M(5, 1), N(4, –1), and P(0, –1). Graph LMPN and its image under reflection in the x-axis. Describe what happens to the coordinates of each vertex compared to the coordinates of its image. • A • B • C • D A.x-coordinates and y-coordinates are opposite. B.x-coordinate is opposite; y-coordinate stays the same. C.x-coordinate stays the same; y-coordinates are opposite. D.x-coordinate becomes y-coordinate and y-coordinate becomes x-coordinate. Lesson 1 CYP2

  14. B. COORDINATE GEOMETRY Quadrilateral LMNP has vertices L(–1, 1), M(5, 1), N(4, –1), and P(0, –1). Graph LMPN and its image under reflection in the origin. Describe what happens to the coordinates of each vertex compared to the coordinates of its image. • A • B • C • D A.x-coordinates and y-coordinates are opposite. B.x-coordinate is opposite; y-coordinate stays the same. C.x-coordinate stays the same; y-coordinates are opposite. D.x-coordinate becomes y-coordinate and y-coordinate becomes x-coordinate. Lesson 1 CYP2

  15. C. COORDINATE GEOMETRY Quadrilateral LMNP has vertices L(–1, 1), M(5, 1), N(4, –1), and P(0, –1). Graph LMPN and its image under reflection in the line y = x. Describe what happens to the coordinates of each vertex compared to the coordinates of its image. • A • B • C • D A.x-coordinates and y-coordinates are opposite. B.x-coordinate is opposite; y-coordinate stays the same. C.x-coordinate stays the same; y-coordinates are opposite. D.x-coordinate becomes y-coordinate and y-coordinate becomes x-coordinate. Lesson 1 CYP2

  16. Lesson 1 CS1

  17. Use Reflections TABLE TENNIS During a game of table tennis, Dipa decides that she wants to hit the ball so that it strikes her side of the table and then just clears the net. Describe how she should hit the ball using reflections. Lesson 1 Ex3

  18. Use Reflections Answer: She should mentally reflect the desired position of the ball in the line of the table and aim toward the reflected image under the table. Lesson 1 Ex3

  19. BILLARDS Dave challenged Juan to hit the 8 ball in the left corner pocket. Should Juan try to have the 8 ball hit the midpoint between the side pocket and the right corner pocket? • A • B A. yes B. no Lesson 1 CYP3

  20. Draw Lines of Symmetry Determine how many lines of symmetry a regular pentagon has. Then determine whether a regular pentagon has a point of symmetry. A regular pentagon has five lines of symmetry. Lesson 1 Ex4

  21. Draw Lines of Symmetry A point of symmetry is a point that is a common point of reflection for all points on the figure. There is not one point of symmetry in a regular pentagon. Answer: 5; no Lesson 1 Ex4

  22. A. Determine how many lines of symmetry an equilateral triangle has. • A • B • C • D A. 1 B. 2 C. 3 D. 6 Lesson 1 CYP4

  23. B. Does an equilateral triangle have a point of symmetry? • A • B A. yes B. no Lesson 1 CYP4

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