Name: ________________________ Class: ___________________ Date: __________ ID: A

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Geometry 2.1-2.5 Worksheet

____ 1. If the pattern indicated below is continued, what would be the total number of cubes in the 8th stage of the

pattern?

a. 204 b. 194 c. 81 d. 9

2. Give one counterexample that shows the conjecture is false.

In a coordinate plane, if the y-coordinate of a point is positive, then the point is in the first quadrant.

Use inductive reasoning to find the next two numbers in each pattern.

3. –9, –5, –1, 3, __, __

4. "If it doesn’t rain, then I will go to the game." What is the underlined portion called in this conditional

statement?

True or False:

5. PointsD, J, andE are coplanar.

6. Line l bisects ∠GBJ .

7. Refer to the following statement: Two lines are perpendicular if and only if they intersect to form a right

angle.

a. Is this a biconditional statement?

b. Is the statement true?

Name: ________________________ ID: A

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Write the pair of conditionals as a biconditional using "if and only if."

8. If 7x2= 112, then x = 4.

If x = 4, then 7x2= 112.

Is the biconditional you wrote True or False? If it is false, rewrite it so it is true.

9. Given the following statements, can you conclude that Marvin listens to the radio on Monday night?

(1) If it is Monday night, Marvin stays at home.

(2) If Marvin stays at home, he listens to the radio.

Decide whether inductive or deductive reasoning is used to reach the conclusion. Explain your

reasoning.

10. The rule in your house is that you must complete all of your homework in order to watch television. You

watched your favorite television show Tuesday night. Therefore, you completed all of your homework on

Tuesday.

Choose the phrase that completes the following statement as stated by the Point, Line, and Plane

Postulates:

____ 11. Two distinct planes ____ intersect in a pair of lines.

a. never

b. always

c. sometimes

d. Point, Line, and Plane Postulates do not address this topic directly.

____ 12. If two distinct lines intersect, their intersection is ____ one point.

a. always

b. never

c. sometimes

d. Point, Line, and Plane Postulates do not address this topic directly.

Use the diagram to write an example of the postulate.

13. If two lines intersect, then their intersection is exactly one point.

Identify the property that makes the statement true.

14. If m∠1 + m∠2 = 25° and m∠1 = 9°, then 9o+ m∠2 = 25

o.

15. "If an obtuse angle is bisected, then two acute angles are obtained." Write the converse of this conditional

statement. Is the converse true?

Name: ________________________ ID: A

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Write the converse of the following statement(s). Then tell whether the converse is True or False.

16. If a statement is true, then its converse is false.

From the given true statements, make a valid conclusion:

17. If there is no more milk, Rita will go to the store.

There is no more milk.

18. If the slipper fits, she is the one.

Cinderella fits in the slipper.

____ 19. Which of the following is an example of the Transitive Property?

a. If y = x − 4, then x − 4 = y.

b. x − 3 = x − 3

c. If x = −3, then x − 4 = −3 − 4.

d. If x − 3 = y and y = −4, then x − 3 = −4.

20. NJ→

bisects ∠HNK.

a. Write an equation that shows the relationship between m∠HNJ and m∠JNK.

b. Solve the equation and write a reason for each step.

c. Find m∠HNK. Explain how you got your answer.