Chapter 9Review for Midterm

Sections 6-10

Ms. Dewey-Hoffman

Pre-Algebra

April 2nd, 2009

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.

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

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?

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

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

Section 7: Construction

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

Bisector

Bisectors cut things in half.

Cut Segments in Half.

Cut an Angle in Half.

Bisecting Segments

Bisecting an Angle

Section 8: TranslationsTransformation = 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

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

Try This...U(-4, -5), V(2, 1): 3 Units Right, 2 Units Down

Give the Rule for the Mapping

1st Determine the Image2nd Find the Difference

0 1 2 3 4 5 6 7 8 9 x

1

9

8

7

6

5

4

3

2

yTranslate Triangle A through

ALabel the image B

B

4 right

2 up

4 right

2 up

4 right

2 up

Label the image BLabel the image B

+ 4, so 4 Right+ 2, so 2 Up

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.

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 (2nd

object).

Remember to figure out the coordinates of the Image.

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.

Section 10: RotationRotation 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.

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.

Here are the Dates for your Journals

• February 4th: 8.1: Relations and Functions• February 5th: 8.2: Equations with Two Variables• February 9th: 8.3: Slope and Y-Intercept• February 10th: 8.4: Writing Rules for Linear Functions• February 11th: 8.5: Scatter Plots• February 19th: 8.6: Solve by Graphing• February 20th: 9.1: Introduction to Solving Systems of Linear Equations• March 2nd: 9.2: Angle Relationships and Parallel Lines• March 3rd: 9.3: Classifying Polygons• March 4th: 9.4: Reasoning Strategy: Draw a Diagram• March 5th: 9.5: Congruence• March 9th: 9.5: Congruence?• March 10th: 9.8: Translations• March 11th: 9.6: Circles• March 16th: 9.7: Construction• March 17th: 9.9: Symmetry and Reflections• March 18th: 9.10: Rotations• April 2nd: Chapter 9, Section 6-10, Review Notes