Instructions: Read Each Question Carefully and Select the Correct Answer s1

SD 9-12 Geometry
03/20/2009

Student Name: ______

Class: ______

Date: ______

Instructions: Read each question carefully and select the correct answer.

SD Geometry – Test, Answer Key, & Study Guide Page 73 of 73

1. Which transformation was performed on the following figure?

A. Rotation

B. Reflection

C. Translation

D. Dilation

2. Choose the graph of the inequality below.
y 9x - 4

3. The following graph represents the equation y = - 4x2 - 4x + 3. Choose the point(s) on the graph that would solve the equation- 4x2 - 4x + 3 = 0.

A. Points R, T, and U

B. Points R and U

C. Point T

D. Point S

4. Choose the system of inequalities represented by the following graph.

5. Choose the correct graph for the equation below.
y = - |x| - 5

6. Which line represents the equation y = - 7?

A. line d

B. line c

C. line b

D. line a

7. What is the measure of any exterior angle of a regular octagon?

A. 135º

B. 45º

C. 22.5º

D. 157.5º

SD Geometry – Test, Answer Key, & Study Guide Page 73 of 73

8. Fill in the missing statement in the proof below.

A. Reflexive Property

B. Transitive Property

C. Corresponding Parts of Congruent Triangles are Congruent

D. Associative Property

SD Geometry – Test, Answer Key, & Study Guide Page 73 of 73

A. 129º

B. 39º

C. 90º

D. 51º

SD Geometry – Test, Answer Key, & Study Guide Page 73 of 73

10.

A. 109º

B. 19º

C. 38º

D. 71º

11.

A. (27, -9)

B. (-1, 5)

C. (27, -7)

D. (3, 5)

12. Which picture shows an interior angle?

13. Which of the following is NOT true?

A. All kites are polygons.

B. All kites have two sets of congruent adjacent sides.

C. All kites have diagonals that are perpendicular.

D. All kites are rhombi.

14. Calculate the sum of the interior angles of the figure below.

A. 180º

B. 540º

C. 360º

D. 720º

15. What is the measure of BAC?

A. 56

B. 34

C. 28

D. There is not enough information given.

16. About which line are the figures symmetric?

C. y = 1

D. y = -1

17. Calculate the midpoint of line segment RS given in the diagram.

A. (-0.5, 6)

B. (6, -0.5)

C. (7.5, 2)

D. (2, 7.5)

18. The mall is 15 miles due south of Jodi's house. The school is 20 miles due east of the mall. What is the shortest distance from Jodi's house to the school?

A. 25 miles

B. 5 miles

C. 35 miles

D. 20 miles

19. Fill in the blank.

If mQSN is equal to 90º , then QSP and PSN are ______.

A. complementary angles

B. supplementary angles

C. vertical angles

D. right angles

20. Fill in the blank.
Quadrilaterals ABCD and WXYZ are congruent.

Segment AD is congruent to segment _____.

A. CD

B. WZ

C. XW

D. BC

21. Point C and point D have symmetry with respect to the y-axis. What are the coordinates of point C when point D is the point (-4, -4)?

A. (-4, -4)

B. (-4, 4)

C. (4, -4)

D. (4, 4)

SD Geometry – Test, Answer Key, & Study Guide Page 73 of 73

22. The following are the front and top views of a building. What is the view from the right side of the building?

SD Geometry – Test, Answer Key, & Study Guide Page 73 of 73

23. What will the coordinates of point A be if figure ABC is rotated clockwise around point D so that point B is at (1, 1)?

A. (1, 0)

B. (3, 0)

C. (4, - 1)

D. (1, 2)

24. These two triangles are congruent.

What is the measurement of QOP?

A. 43º

B. 90º

C. 47º

D. 3º

25. Choose the graph that represents the equation.

SD Geometry – Test, Answer Key, & Study Guide Page 73 of 73

26. Solve the system of equations by graphing.
x + 2y = 7
2x - y = -1

A. (-1, 7)

B. (3, 1)

C. (1, 3)

D. (7, -1)

27. A triangle has sides which are 9, 40, and 41 millimeters long. How could you determine if this triangle is or is not a right triangle?

28. Find the distance between point R (-1, 0) and point Q (3, 2).

SD 9-12 Geometry
Answer Key
03/20/2009

1. B Spatial Relationships - B

2. C Graph Inequalities

3. B Solve Quadratic Equations by Graphing

4. B Graph Systems of Inequalities

5. D Graph Absolute Value

6. A Graph Equations: Constant

7. B Angles and Bisectors

8. B Proofs

9. B Perpendicular Bisector

10. D Angles - D

11. B Translation: Ordered Pair

12. A Interior Angles: Polygons - A

13. D Properties of Kites/Trapezoids

14. C Interior Angles: Polygons - B

15. C Congruence (AAS/ASA/SAS) - B

16. C Symmetry - C

17. C Midpoint

18. A Triangles - B

19. A Angles - B

20. B Congruency - C

21. C Symmetry - D

22. B Spatial Relationships - C

23. D Transformations

24. C Congruence (AAS/ASA/SAS) - A

25. C Graphing Equations - A

26. C Graphing Equations - B

27. D Pythagorean Theorem

28. C Distance Formula

Study Guide
SD 9-12 Geometry
03/20/2009

Spatial Relationships - B
Spatial relationships include geometric transformations. A transformation is a mapping of a point or shape to a new location or orientation. Transformations include reflections, rotations, dilations, or translations. All transformations except for dilations preserve the original size and shape of the image.

First, we'll define each of the transformations mentioned above:
A translation is sliding of a figure from one location to another. (Also called a "slide.")
For example:

A dilation is the image of a figure similar to the original figure. It can be thought of as shrinking or enlarging a figure.
For example:

A reflection is flipping a figure across a line, just as you would reflect your hand in a mirror.
For example:

A rotation is the movement of a figure in a circular motion around a point. If you drew a figure on a piece of paper, put the paper on the desk, and turned the paper, you would have a rotation.
For example:

It might be helpful to draw figures on a piece of paper, and rotate them to illustrate rotation of figures.
Example 1: What transformation was performed on the following figure?

The answer is a rotation.
We can use a coordinate plane to show where the parts of a shape are. If we draw the x- and y-axes, we divide the coordinate plane into four parts, each called a quadrant. The quadrants are numbered as follows:

If we reflect a figure (triangle ABC) over the x-axis, what are the coordinates of the reflected figure? (Use "prime" notation A' to identify the image. A' can be read "A prime.")

A translation moves a figure to another location. Below is triangle ABC moved 3 units left and 5 units down. We can find the coordinates as follows:

Graph Inequalities
An inequality is a number sentence that uses is greater than or is less than symbols. For example, 6n < 4 and y 2x - 3 are inequalities.

When graphing an inequality, the student should mentally replace the inequality symbol with an equal sign in order to graph the inequality as an equation. Then use the table below to decide the type of line that should be used when drawing the graph.

A dashed line tells the reader that the values on the line ARE NOT included in the inequality. A solid line tells the reader that the values on the line ARE included in the inequality.
Example 1:
Graph the inequality.
y > - 4x - 6

Step 1: Graph the line that is represented by the inequality. (Remember to mentally replace the > with =.) This equation is given in y = mx + b form (slope-intercept form), where m is the slope and b is the y-intercept. Plot the y-intercept, (0, - 6), then use the slope, - 4, to move up 4 units and to the left 1 unit. The is greater than symbol (>) is used, refer to the chart above to see that this symbol requires a dashed line. Connect the two points using a dashed line.
Step 2: Choose a test point to determine which side of the line should be shaded. The most common test point to use is (0, 0), but it does not matter what point is used. Substitute the test point into the inequality and simplify.
• If the test point makes the inequality true, shade the side of the line that includes the test point.
• If the test point makes the inequality false, shade the side of the line that does not include the test point.
In this case, the test point makes the inequality true.
Step 3: Since the test point makes the inequality true, shade the side of the dotted line that includes the point (0, 0).
Answer:

Example 2:
Determine the correct inequality for the graph below.

Step 1: Determine the equation of the line. In this case, the y-intercept is at (0, - 6) and the slope appears to be up 1, over 4 (or ?), as can be seen by points at (8, - 4) and (4, - 5). Therefore, the equation of the boundary line is y = (?)x - 6.
Step 2: Use the table on page 1 to determine which type of inequality symbol to use (<, >, , or ). The line on the graph is solid, so the or symbol must be used.
Step 3: Choose a test point from the shaded side of the line and substitute it into each inequality to determine which of the two inequalities is correct. A good test point to use is (0, - 8), since (0, - 8) is included in the shaded area of the graph. Since y = (?)x - 6 is true when (0, - 8) is used as the test point, it is the correct inequality.

To reinforce this skill, create of set of index cards with inequalities written on them and another set with the graphs of the equations drawn and shaded. Shuffle the cards and lay them face-down on a table in columns and rows. Have the student turn two cards over at a time and try to match the inequality to the correct graph. If the two cards do not match, the next player can try to make a match. If the cards match, the player keeps the two cards and gets a chance to make another match. The player with the most matches at the end of the game wins.

Solve Quadratic Equations by Graphing
A quadratic equation is a function that contains polynomial expressions for which the highest power of the unknown variable is two.

Quadratic functions are written in the form:
y = ax2 + bx + c or f(x) = ax2 + bx + c
f(x) is read "f of x."
Below are a few examples of quadratic functions:
y = x2 + 3x - 4 g(x) = - 2x2 + 6 f(x) = 5x2 - 2x
Graphs of quadratic functions are always in the shape of a parabola. Parabolas can open up or open down. Examples of each are shown below.

Factoring, using the quadratic formula, and graphing are the three main methods for solving quadratic equations. This skill focuses on solving quadratic equations by graphing. To solve quadratic equations, it is necessary to find the values for x in which y equals zero. These values occur at the x-intercept(s), or the point(s) where the graph crosses the x-axis. The x-intercepts are of the form (x, 0), where the y-value equals zero. X-intercepts can occur at two points, one point, or no points.

Example 1:
The following graph represents the equation y = - 3x2 - 3x + 1. Choose the point(s) on the graph that would solve the equation - 3x2 - 3x + 1 = 0.

Solution:
The x-intercepts are the solutions to the quadratic equation. Therefore, points J and M would solve - 3x2 - 3x + 1 = 0.
Answer: Points J and M.

Graph Systems of Inequalities
An inequality is a number sentence that uses is greater than or is less than symbols. For example, 6n < 4 and y 2x - 3 are inequalities.