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

Test 2 Review
Geometry Pre-AP
Due Test Day!
Name __________________________
Section: 2.1 – 2.3, 2.5 – 2.7
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.
_____5. For all x values greater than or equal to zero, 2 x is even.
_____6. If x is a prime number, then x + 1 is not prime.
_____7. If X, Y, and Z are collinear points, then XY + YZ = XZ.
8. Identify the hypothesis and conclusion of the following conditional statement:
“The show is cancelled if it rains”.
9. 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.
10. If the hypothesis of a conditional statement is true, and the conclusion is false, then the statement is ___?
11. If the hypothesis of a conditional statement is false, and the conclusion is true, then the statement is ___?
12. If the hypothesis of a conditional statement is false, and the conclusion is false, then the statement is ___?
13. Which statement is always logically equivalent to the conditional? ________________________________
14. Which statement is always logically equivalent to the inverse? __________________________________
Write the conditional and converse statements that make up each biconditional statement. Then determine the
truth value of the biconditional statement.
15. An angle is a right angle if and only if its measure is 90 degrees. True / False
Conditional: _________________________________________________________________
Converse: ___________________________________________________________________
16. A parallelogram is a rectangle if and only if it has four right angles. True / False
Conditional: _________________________________________________________________
Converse: ___________________________________________________________________
17. Write FOUR conditional statements that describe the relationship between the various groups of musicians
as shown in the Venn Diagram.
Musicians
Band
Chorus
1.
2.
3.
4.
Jazz Band
18. Using a two–column proof, solve the following equations and justify each step!
a.
5 – x = -3(2x + 4)
4x  6
2  4
3
b.
19. Fillin the blanks to complete the two-column proof.
2 3
Prove:  1 and  3 are supplementary
Given:
1
1
Statements
1.
2 3
2
Justifications
1. Given
2. m  2 = m  3
2.
3.
3. Linear Pair Theorem
4. m  1 + m  2 = 180
4. Def. of ___________ angles
5. m  1 + m  2 = 180
5.
6.
6. Def. of Supplementary
3
Complete the following two-column proof. NUMBER EACH STEP!
20. Given: X is the midpoint of segment AY, and
Y is the midpoint of segment XB.
A
X
Y
B
Prove: AX  YB
Identify the property that justifies each statement.
ST  XY , then XY  ST
21. If 18 = 9x, then x = 2
25. If
22. If 2x = y and y = 7, then 2x = 7
26. If x = z, then xy = yz
23. m  DEF = m  DEF
27. If mn + mp, then m(n + p)
24.
 X   P,  P   D. So  X   D.
28. If AB + CD = EF + GH and AB + CD = MN
and EF + GH = OP, then MN = OP
29. Which theorem correctly justifies the conclusion that
 1   4?
_____________________________________________