Chapter 9 Review Lessons 6 10
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This document provides a summary of key concepts from sections 6-10 of chapter 9 in preparation for a midterm exam. It includes definitions and examples of circles, translations, symmetry, reflections, and rotations. Students are instructed to complete example problems in their notes and identify 3 things they learned or needed review. The midterm will cover material from specific pages and math journals are due.
Chapter 9 Review Lessons 6 10
- 1. Chapter 9 Review for Midterm Sections 6-10 Ms. Dewey-Hoffman Pre-Algebra April 2nd, 2009
- 2. What to Write Down Do all of the example problems in your notes. By the end of class, have written down 3 things that you had either forgotten or learned from today.
- 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?
- 5. Try These: Find the Circumference, Use 3.14 for Pi Diameter of 25 Feet Radius of 7.8 Centimeters Diameter of 100 Meters 78.5 Feet 48.984 cm 314 Meters
- 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.
- 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.
- 20. Here are the Dates for your Journals February 4 th : 8.1: Relations and Functions February 5 th : 8.2: Equations with Two Variables February 9 th : 8.3: Slope and Y-Intercept February 10 th : 8.4: Writing Rules for Linear Functions February 11 th : 8.5: Scatter Plots February 19 th : 8.6: Solve by Graphing February 20 th : 9.1: Introduction to Solving Systems of Linear Equations March 2 nd : 9.2: Angle Relationships and Parallel Lines March 3 rd : 9.3: Classifying Polygons March 4 th : 9.4: Reasoning Strategy: Draw a Diagram March 5 th : 9.5: Congruence March 9 th : 9.5: Congruence? March 10 th : 9.8: Translations March 11 th : 9.6: Circles March 16 th : 9.7: Construction March 17 th : 9.9: Symmetry and Reflections March 18 th : 9.10: Rotations April 2 nd : Chapter 9, Section 6-10, Review Notes