Download Determine if the following conjectures are True or False. If False

Geometry Pre-AP
Name __________________________
Ch. 2 Review
Determine if the following conjectures are True or False. If False, give a counterexample.
_____1. The sum of any three consecutive integers is three times the second number.
_____2. All prime numbers are odd.
_____3. If the product of two numbers is positive, then the two numbers must both be positive.
_____4. A number is divisible by four if the last two digits of that number are divisible by four.
Describe the following patterns, then find the next two terms.
8.
5 25 125 625
,
,
,
, _______ , _______
9
16
4
1
9. 2, 20, 10, 100, 50, _______, ________
11. A speeding ticket costs $40 plus $5 per mile an hour over the speed limit. Lynne mentions to Frank that she
was given a ticket for $75. Frank concludes that Lynne was driving 7 mi/h over the speed limit.
Inductive
Deductive
(Circle one)
12. Kyle is new to Dripping Springs. He notices that the drum line marched through the school for the two away
football games we have had. This Friday is an away game, so he concludes that the drum line will be marching
through the school.
Inductive
Deductive
(Circle one
13. Identify the hypothesis and conclusion of the following conditional statement:
“The show is cancelled if it rains”.
14. Write a conditional statement from the sentence “Parallel lines do not intersect”.
_________________________________________________________________________________.
Now, write the a. converse, b. inverse, and c. contrapositive of that statement, then determine the truth value
of each one.
a.
b.
c.
15. Which statement is always logically equivalent to the conditional? ________________________________
16. Which statement is always logically equivalent to the inverse? __________________________________
Write the conditional and converse statements that make up the biconditional statement. Then determine
the truth value of the biconditional statement.
18. An angle is a right angle if and only if its measure is 90 degrees. True / False
Conditional: _________________________________________________________________
Converse: ___________________________________________________________________
17. Identify whether each statement is valid or invalid; if valid, identify whether the Law of Detachment or Law
of Syllogism was used.
a.
Given: Right angles are congruent.
Conclusion:
 1 and  2 are right angles.
1  2
b. Given: If Dante obtains a part time job, he can afford a car payment. Dante can afford a car payment.
Conclusion: Dante obtained a part time job.
c.
Given: If Dalila finishes her chores, then she will get her allowance. If Dalila receives her allowance, she
will purchase a new shirt.
Conclusion: If Dalila finishes her chores, then she will purchase a new shirt.
Identify the property that justifies each statement.
ST  XY , then XY  ST
20. If 18 = 9x, then x = 2
21. If
22. If 2x = y and y = 7, then 2x = 7
23. If x = z, then xy = yz
24. m  DEF = m  DEF
25. If mn + mp, then m(n + p)
26.
 X   P,  P   D. So  X   D.
27. If AB + CD = EF + GH and AB + CD = MN
and EF + GH = OP, then MN = OP
28. Using a two–column proof, solve the following equations and justify each step!
5 – x = -3(2x + 4)
Statements
Justification
4x  6
2  4
3
29.
Statements
Justification
Complete the following two-column proof.
30. Given: m  1 + m  3 = 180°
Prove:
1  4
Statements
31. Given:
Justification
2  3
AC is perpendicular to BC
Prove:  3 is complementary to  1
Statements
Justification