Foundations for Geometry s1

Name Date Class

Tools of Geometry

Quiz

Holt McDougal Analytic Geometry

Name Date Class

Choose the best answer.

Refer to the figure for Exercises 1 and 2.

1. Which represents the name of the ray whose endpoint is K and that passes through R?

A C

B D

2. In the diagram, how many different rays have endpoint R?

F 1 H 3

G 2 J 4

Refer to the figure for Exercises 3 and 4.

3. What is MP?

A 1 C 4

B 2 D 5

4. What is LP?

F -7.5 H 2.5

G -2.5 J 7.5

5. An angle whose measure is 70° is what type of angle?

A acute C obtuse

B right D straight

6. bisects ÐFGH, mÐFGJ = (7x - 9)°, and mÐHGJ = (2x + 36)°. What is mÐFGH?

F 43° H 86°

G 54° J 108°

7. An angle measuring 22° is bisected. What is the measure of the angles that are formed?

A 11° C 33°

B 22° D 44°

8. What is the next letter in the sequence?
D, H, L, P, . . .

F Q H S

G R J T

9. Which is the counterexample that proves the conjecture false?

“If two rays have the same endpoint, then they are opposite rays.”

A C

B D

10. Identify the hypothesis of the conditional statement “Two angles are complementary if the sum of their measures is 90 degrees.”

F if

G Two angles are complementary

H the sum of their measures is
90 degrees

J Two angles are complementary if the sum of their measures is 90 degrees.

11. Which conditional statement has the same truth value as this statement?
“The sum of two odd numbers is even.”

A If two even numbers are added, then their sum is even.

B If an even and odd number are added, then their sum is even.

C If two even numbers are multiplied, then their product is odd.

D If two odd numbers are multiplied, then their product is even.

Holt McDougal Analytic Geometry

Name Date Class

Holt McDougal Analytic Geometry

Name Date Class

Tools of Geometry

Quiz continued

Holt McDougal Analytic Geometry

Name Date Class

Use the figure for Exercises 12–15.

12. Name a line.

13. Name a segment on line n.

14. Name a ray with endpoint A.

15. Name the intersection of and

16. Z is in the interior of ÐWXY.
If mÐWXZ = 110°, and mÐZXY = 20°, what is mÐWXY?

17. ÐA and ÐB are complementary.
mÐA = 29°. Find mÐB.

18. Find the next item in the pattern.
2, 5, 8, 11, 14, . . .

19. Show that the conjecture is false by finding a counterexample. When the letters i and e appear next to each other in a word, the letter i always comes before the letter e.

20. Identify the hypothesis and conclusion of the statement “If it is raining, then there are clouds in the sky.”

21. Given: If Lewis earns a scholarship, he can go to college. Lewis earns a scholarship.
Conjecture: Lewis can go to college. Determine whether the conjecture is
valid by the Law of Detachment.

Holt McDougal Analytic Geometry

Name Date Class

Algebraic and Geometric Proofs

Quiz

Holt McDougal Analytic Geometry

Name Date Class

Choose the best answer.

1. Consider the related biconditional statement for the conditional statement “If Shelly lives in Texas, then she lives in the United States.”

Which of the following statements is true about the related biconditional statement?

A The biconditional is true because the conditional is true.

B The biconditional is false because the conditional and its converse are false.

C The biconditional is true because the conditional and its converse are true.

D The biconditional is false because the converse of the conditional is false.

2. If r + 14 = -9, what justifies r = -23?

F Transitive Property of Equality

G Subtraction Property of Equality

H Symmetric Property of Equality

J Reflexive Property of Equality

3. If = 8, what justifies
x - 1 = 16?

A Subtraction Property of Equality

B Division Property of Equality

C Transitive Property of Equality

D Multiplication Property of Equality

4. If 5 = 2k, what justifies 2k = 5?

F Multiplication Property of Equality

G Division Property of Equality

H Symmetric Property of Equality

J Reflexive Property of Equality

5. Which completes the statement?
If 6x = 5 and d = 6x, then ______by
the Transitive Property of Equality.

A d = 5 C 6x = d

B x = D x =

6. Which completes the statement?
If then ______by the Symmetric Property of Congruence.

F RS = GH H

G J

7. Given: L bisects ; M bisects

Prove: KL = MN

Proof:
Since L bisects and M bisects by definition of bisect, and Then, by the ?, Finally,
KL = MN by the definition of congruent segments.Which completes the proof?

A Common Segments Theorem

B Transitive Property of Congruence

C Segment Addition Postulate

D Symmetric Property of Congruence

Holt McDougal Analytic Geometry

Name Date Class

Algebraic and Geometric Proofs

Quiz continued

Holt McDougal Analytic Geometry

Name Date Class

8. Given: Ð1 @ Ð4

Prove: Ð2 @ Ð3

Proof:

Statements / Reasons
1. Ð1 @ Ð4 / 1. Given
2. Ð1 and Ð2 are supp.,
and Ð3 and Ð4 are
supp. / 2. Lin. Pairs
Thm.
3. Ð2 @ Ð3 / 3. ?

Which completes the proof?

F Transitive Property of Congruence

G Vertical Angles Theorem

H Congruent Supplements Theorem

J Angle Addition Postulate

9. For the following statement, what is the “Prove” statement?
If ABCD is a rhombus, then it is a parallelogram.

A ABCD is a quadrilateral.

B ABCD is a rhombus.

C ABCD is a parallelogram.

D ABCD is not a square.

10. Use the Reflexive Property of Congruence to complete the statement “ÐA @ ______.”

11. Complete the sentence “A ______is any statement that you can prove.”

12. What is the reason for Step 2?

Statements / Reasons
1. Ð1 @ Ð2 and
Ð2 @ Ð3. / 1. Given
2. mÐ1 = mÐ2 and mÐ2 = mÐ3. / 2. ?
3. mÐ1 = mÐ3 / 3. Trans. Prop. of =
4. Ð1 @ Ð3 / 4. Def. of @

13. The box is part of a flowchart proof. Identify the statement.

14. Write True or False. A paragraph proof is less formal than a two-column proof, so you do not need to include every step.

Holt McDougal Analytic Geometry