Download Geometry Pre-AP Name Test 2 Review Determine if the following

Geometry Pre-AP
Name __________________________
Test 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.
_____5. For all x values greater than or equal to zero, 2x 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.
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, _______, ________
10. Use the following statements to write a compound statement for each conjunction or disjunction. Then find its
truth value.
p: A plane contains at least three noncollinear points
q: A square yard is equivalent to three square feet.
R: The sum of the measures of two complimentary angles is 180º.
a.
c.
b.
Create a truth table for 10 (b)
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. Draw a valid conclusion from the given statements, if possible. Then state whether your conclusion was drawn
using the Law of Detachment or the Law of Syllogism. If no valid conclusion can be drawn, write no valid conclusion
and explain your reasoning
a. Given: If a quadrilateral has diagonals that bisect each other, then it is a parallelogram.
The diagonals of quadrilateral PQRS bisect each other.
b. Given: If Liana struggles in science class, then she will receive tutoring. If Liana stays after school on
Thursday, then she will receive tutoring.
15. 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.
16. Which statement is always logically equivalent to the conditional? ________________________________
17. Which statement is always logically equivalent to the inverse? __________________________________
18. Write TWO conditional statements that describe the relationship between the various groups of musicians as
shown in the Venn Diagram.
Musicians
1.
Band
Chorus
2.
Jazz Band
Write the conditional and converse statements that make up each biconditional statement. Then determine
the truth value of the biconditional statement.
19. An angle is a right angle if and only if its measure is 90 degrees. True / False
Conditional: _________________________________________________________________
Converse: ___________________________________________________________________
20. A parallelogram is a rectangle if and only if it has four right angles. True / False
Conditional: _________________________________________________________________
Converse: ___________________________________________________________________
Identify the property that justifies each statement.
ST  XY , then XY  ST
21. If 18 = 9x, then x = 2
22. If
23. If 2x = y and y = 7, then 2x = 7
24. If x = z, then xy = yz
25. m  DEF = m  DEF
26. If mn + mp, then m(n + p)
27.
 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. 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
30.
Statements
Justification
Complete the following two-column proof.
31. Given: m  1 + m  3 = 180°
Prove:
1  4
Statements
32. Given:
Justification
2  3
AC is perpendicular to BC
Prove:  3 is complementary to  1
Statements
Justification
XB bisects  AXC
 1 is complementary to  3
33. Given:
Prove:
XB is perpendicular to XD
Statements
Justification