GeometryChapter 2 TestPage 1
Show work whenever possible. Write the final answer in the space provided.
Apply Inductive and Deductive Reasoning
1) Use the given pattern to find the next two terms in the sequence, and then describe the pattern.
3, 0, -3, 0, 3, 0 …
1a) Next Terms: ______, ______
1b) Pattern: ______
2)Each figure consists of squares constructed from unit segments connecting each point.
2a)Complete the table.
Figure / 1 / 2 / 3 / 4 / 5Picture / / / /
Number of
Unit Segments / 2 / 7
Number of
Unit Squares / 0
2b) Describe the pattern for the number of segments in part 2a).
2c) Describe the pattern for the number of squares in part 2a).
2d) Find the number of squares and segments for the 8th figure in part 2a).
Segments: ______Squares: ______
3) Given the true conditional statement, identify the parts of the conditional statement and state each related statement.
Conditional: I get wet if I am standing in the rain.
3a) State the hypothesis:
3b)State the conclusion:
For problems 3c) through 3f), state the related conditional statement, determine if the statement is true or false and explain why the statement must be true or false.
3c)If – Then
Statement:
True or False? Explain.
3d)Inverse
Statement:
True or False? Explain.
3e)Converse
Statement:
True or False? Explain:
3f)Contrapositive
Statement:
True or False? Explain.
4) Only one of the following statements can be written as a true biconditional statement. Circle the correct true biconditional statement.
[A] If two angles sum to 90o, then they are supplementary.
[B] If an angle is a right angle, then it measures 90.
[C] If an angle measures 100, then it is obtuse.
[D] If angles measure 30 and 60, then they are complementary.
5) A problem including student work from a recent test is shown below. Determine if the student work is correct. If the work is incorrect, write a statement which would be correct.
Conditional Statements:
If Jose gets good grades, then he will graduate.
If Jose comes to school, then he will see his friends.
If Jose does his homework, then he will get good grades.
5a) Jose comes to school. Using the Law of Detachment, what can you conclude?
Correct? Yes or No
If incorrect, correct the statement.
5b) The same student was asked to use the Law of Syllogism to write a new conditional statement. Is the student's statement shown below correct? If it is incorrect, correct the statement.
Correct? Yes or No
If incorrect, correct the statement.
Understanding Geometric Relationships and Writing Proofs6)Planes A and B intersect as shown. Points C and D lie on plane A. Points X, Y and Z lie on plane B.
True or False: (Circle the correct choice.)
6a) is on plane A.T or F
6b) Points C, D, X and Z are coplanar. T or F
6c) intersects line EF. T or F
6d) intersects line CD. T or F
Complete the sentence:
6e) The intersection of plane A and plane B is ______.
7)Select the correct property for each statement. Mark the letter of the appropriate choice in the blank.
7a)If = , then = _____
7b) If BC = CD and CD = EF, then BC = EF _____
7c)For any segment AB, AB = AB _____
7d)If = 30o, then 3() = 90o. _____
7e)If x + 2 = y + 5, then x = y + 3. _____
8) Solve the equation and state the reason for each step: -2x + 6(2x – 3) = 4x + 6
Step: / Reason:-2x + 6(2x – 3) = 4x + 6Given
9)Write an equation and solve for the indicated value. Write a sentence explaining the theorem or property used to develop the equation.
9a)Equation and solution:x = ______
Explain the theorem or property used.
9b)Equation and solution: x = ______y = ______
Explain the theorem or property used.
10)Complete each proof.
10a)Given: 1 and 2 are supplementary. m 1 = 78o.
Prove:m2 = 102o.
10b)Given:
Prove:
Reassessment: Use Segment Postulates and Formulas11)Points C and D are between points A and B on . D is between C and B. Given AC = 3x + 1,
CD = 2x + 4, BD = 5x – 15, and AB = 50,
Draw a picture:
11a)find x.11b)find AC.
x = ______AC = ______
11c)find CB.11d) Is point C the bisector of ? Yes or No
Explain:
CB = ______
12)Use the graph below to find:
12a) the distance between A and B.
12b) the midpoint of A and B.
12c) If M is the midpoint of , find the coordinates of C.
13)Use the image below and proper notation to:
13a) name the plane.
13b) write two names for a line that lies in the plane.
13c) name the line which does not lie in the plane.