Chapter 9 Review, Lessons 6-10

1. Chapter 9 Review for Midterm Sections 6-10 Ms. Dewey-Hoffman Pre-Algebra April 2nd, 2009

3. Section 6: Circles Circle: a bunch of points, all the same distance from a central point.

4. Circumference, π, and Diameter Circumference, Pi, and Diameter are Related If Diameter changes, Circumference Changes. Diameter x Pi = Circumference Pi = 3.14...... When Diameter is 1, Circumference is 3.14. If they only give you radius, how do you find diameter?

6. Pie Graphs To find the Degree Measurements of a Section of a Pie Graph: 1) Find the Percentage of your item (like how long you sleep a day). 9 / 24 = 38% 2) Make the Percentage a Fraction 38/100. 3) Make a Proportion! 38/100 = X/360. 4) Solve for X, it will be the Degree Measurement of the Amount you Sleep. 38 x 360 = 100X. 13,680/100 = 136.8 degrees

7. Section 7: Construction Perpendicular: two intersecting lines that form a 90 degree angles.

8. Bisector Bisectors cut things in half. Cut Segments in Half. Cut an Angle in Half.

9. Bisecting Segments

10. Bisecting an Angle

11. Section 8: Translations Transformation = Movement of an Object. Translation = Moves all the points of an Object the same distance and direction. Image = The Second Object after you've moved the first. Label the IMAGE with PRIMARY Notation. A -> A', A' is the Image to A

12. Describing Translations Look at the First Point. Then Look where the Image is going to be. Determine the Difference between the Y values and the X values. A (-4, 8) A' (2, 7) Mapping: (x, y) -> (x + , y + ) Y: 7 – 8 = -1 X: 2 - (-4) = 6 (x, y) -> (x + 6, y + -1) Subtract the Original Object Position from the (Second, Primary) Image. Image – Original

13. Try This... U(-4, -5), V(2, 1): 3 Units Right, 2 Units Down Give the Rule for the Mapping 1 st Determine the Image 2 nd Find the Difference

14. Label the image B Label the image B Label the image B + 4, so 4 Right + 2, so 2 Up 0 1 2 3 4 5 6 7 8 9 x 1 9 8 7 6 5 4 3 2 y Translate Triangle A through A B 4 right 2 up 4 right 2 up 4 right 2 up

15. Section 9: Symmetry & Reflection Reflectional Symmetry = A figure has it if half of the figure is a mirror image of the other half. Line of Symmetry = Divides the Image in Half.

16. Reflection Reflection flips an image over a Line of Reflection. The reflection is Congruent to the original object. Each point that makes up the original object is the same distance from the Line of Reflection as the Image (2 nd object). Remember to figure out the coordinates of the Image.

17. Reflection Find the points of the reflected triangle from W(-1,-1), X(0, 0), Y(-5, 0) over the line of reflection at y=2. Remember, Y = horizontal line, X = vertical line.

18. Section 10: Rotation Rotation is the same as Reflection, but instead of a Line of Reflection, it has a Degree of Rotation. Center of Rotation = Point that the object rotates around. Rotational Symmetry = An object has it if you can turn it and it still looks the same.

19. Chapter 9 Midterm Tomorrow Bring a Compass and Straightedge!!! The test will either be from page 499 or page 718. MATH JOURNALS DUE TOMORROW!!! Get notes you may have missed from a friend.