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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 . - PowerPoint PPT Presentation

### Transcript of 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 ABC, if mC = 90, AB = x, AC = y, and CB = z, then find cos A.In ABC, if mC = 90, AB = x, AC = y, and CB = z, then find sin A.In ABC, if mC = 90, AB = x, AC = y, and CB = z, then find tan B.

• Lesson 1 MI/Vocabreflectionline of reflectionisometryline of symmetrypoint of symmetryDraw reflected images.Recognize and draw lines of symmetry and points of symmetry.

• Lesson 1 Ex1Reflecting a Figure in a LineDraw the reflected image of quadrilateral WXYZ in line p.Step 1 Draw segments perpendicular to line p from each point W, X, Y, and Z.

• Lesson 1 Ex1Reflecting a Figure in a LineStep 3 Connect 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.

• ABCDLesson 1 CYP1Draw the reflected image of quadrilateral ABCD in line n.

• Lesson 1 Ex2A. 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.Reflection on a Coordinate PlaneUse 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 Ex2Plot 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).Reflection on a Coordinate Plane

• Lesson 1 Ex2B. 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.Reflection on a Coordinate PlaneUse 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 Ex2Plot 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)Reflection on a Coordinate Plane

• Lesson 1 Ex2C. 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.Reflection on a Coordinate Plane

• Lesson 1 Ex2Reflection on a Coordinate Plane

• Lesson 1 Ex2Answer: The x-coordinates becomes the y-coordinate and the y-coordinate becomes the y-coordinate. That is, (a, b) (b, a).Reflection on a Coordinate PlaneA(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 vertices and connect to form the image A' B' C' D'.

• Lesson 1 CYP2ABCDA.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.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.

• Lesson 1 CYP2ABCDA.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.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.

• Lesson 1 CYP2ABCDA.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.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.

• Lesson 1 CS1

• Lesson 1 Ex3TABLE 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.Use Reflections

• Lesson 1 Ex3Answer: 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.Use Reflections

• Lesson 1 CYP3ABBILLARDS 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.yesB.no

• Lesson 1 Ex4Determine how many lines of symmetry a regular pentagon has. Then determine whether a regular pentagon has a point of symmetry.Draw Lines of SymmetryA regular pentagon has five lines of symmetry.

• Lesson 1 Ex4A 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; noDraw Lines of Symmetry

• ABCDLesson 1 CYP4A.1B.2C.3D.6A. Determine how many lines of symmetry an equilateral triangle has.

• Lesson 1 CYP4ABA.yesB.noB. Does an equilateral triangle have a point of symmetry?

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