Geometry Chapter 2 Test Review
Name_________________________
____
1. Based on the pattern, what are the next two terms of the sequence?
8, 15, 22, 29, . . .36 and 43(the pattern adds 7)
____
2. Based on the pattern, what is the next figure in the sequence?
A square should come next!
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3. What conjecture can you make about the thirteenth term in the pattern A, B, A, C, A, B, A, C?
The pattern repeats every 4 terms…so the 13th term is A since the 12th would be C.
____
4. Laisha’s Internet Services designs web sites and recently began a weekly advertising campaign. Laisha noticed
an increase in her customers over a period of five consecutive weeks. Based on the pattern shown in the graph,
make a conjecture about the number of customers Laisha will have in the 8th week. 15 customers
10
y
Number of Customers
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
x
Week
____
5. What is a counterexample for the conjecture?
Conjecture: Any number that is divisible by 5 is also divisible by 10. 15 is not divisible by 10.
____
6. Identify the hypothesis and conclusion of this conditional statement. Write the converse, inverse and
contrapositive of the conditional.
If two lines do not intersect at right angles, then the two lines are not perpendicular.
Hypothesis
Conclusion
Converse: If two lines are not perpendicular, then the two lines do not intersect at right angles.
Inverse:
If two lines intersect at right angles, the the two lines are perpendicular.
Contrapositive: If two lines are perpendicular then the two lines intersect at right angles.
____
7. Another name for an if-then statement is a Conditional. Every conditional has two parts, what are they?
Hypothesis and Conclusion
____
8. Write this statement as a conditional in if-then form:
All rectangles have four sides.
If it’s a rectangle then it has four sides.
____
9. Make a statement that is a counterexample for the following conditional?
If you live in Springfield, then you live in Illinois.
You could live in Springfield, Missouri. (There are other Springfield’s not in Illinois.)
____ 10. What is the converse of the following conditional?
If a point is in the first quadrant, then its coordinates are positive.
If the coordinates are positive, then the point is in the first quadrant.
____ 11. For the following true conditional statement, write the converse. If the converse is also true, combine the
statements as a biconditional.
If x = 4, then x2 = 16.
Converse: If x2 = 16, then x = 4 False, x = -4 would be true as well.
____ 12. What is the converse of the following true conditional? The inverse? The contrapositive?
If two lines are parallel, they do not intersect.
Converse: If two lines do not intersect, then they are parallel.
Inverse: If two lines are not parallel, then they do intersect.
Contrapositive: If 2 lines do intersect, then they are not parallel.
____ 13. Determine whether the conditional and its converse are both true. If both are true, combine them as a
biconditional. If either is false, give a counterexample.
If an angle is a acute angle, its measure is less than 90.
If an angle measure is less than 90, the angle is a acute angle. Both are true!
Biconditional: An angle is an acute angle if and only if its measure is less than 90.
____ 14. Write the two conditional statements that make up the following biconditional.
I drink coffee if (and only if) it is breakfast time.
If I drink coffee, then it is breakfast time.
If it is breakfast time, then, I drink coffee.
____ 15. One way to show that a statement is NOT a good definition is to find a counterexample.
____ 16. Provide a counterexample to the following faulty definition?
A square is a figure with four sides.
Rectangles have four sides as well.
____ 20. What is the value of x? Identify the missing justifications.
,
, and
.
P
R
Q
S
Drawing not to scale
x + 7 + x + 3 = 100
2x + 10 = 100
2x = 90
x = 45
a. Angle Addition Property
b. Substitution Property
c. Simplify
d. Subtraction
e. Division Property of Equality
____ 21.
bisects
= 6x.
6x = 2x + 24 + 2x + 24
6x = 4x + 48
2x = 48
x = 24
= 2x + 24. Find
= 2x + 24 = 2(24) + 24 = 48 + 24 = 72
____ 22. Transitive Property of Congruence: Fill in the Blank.
CD  GH .
If
____ 23. Substitution Property of Equality: Fill in the Blank.
If
, then 8x + 3 = 12.
____ 24. Name the Property of Congruence that justifies the statement:
If
. Symmetric.
____ 25. Name the Property of Congruence that justifies this statement:
If
. Transitive.
____ 26. Complete the two-column proof.
Given:
Prove:
a. Given
b. Substitution
c. Subtraction
d. Division
e. Symmetric
____ 27. What is the value of x?
3x -10 = 149
3x = 159
x = 53
(3x – 10)º
149 º
Drawing not to scale
____ 28.
m1  3 7
Find .
1
4
2
3
Drawing not to scale
____ 29. Find the values of x and y.
7x + 7 = 112
7x = 105
x = 15
4y + 112 = 180 (linear pair)
4y = 68
y = 17
4y°
112°
7x + 7°
Drawing not to scale
30.Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample.
If x = 4, then x2 = 16.
Converse:
If x2 = 16, then x = 4. (False, since it could be -4)
31.Complete the paragraph proof.
Given:
are supplementary, and
are supplementary.
Prove:
By the definition of supplementary angles,
by _transitive (c). Subtract
You get
m3 (d), or
3 (e).
180 (a) and
from each side.
180 (b). Then
32. What are the converse, inverse, and contrapositive of the following true conditional?
If a figure is a square, then it is a parallelogram.
Converse:
If it’s a parallelogram, then it’s a square.
Inverse:
If it’s not a square, then it’s not a parallelogram.
Contrapositive: If it’s not a parallelogram, then it’s not a square.
33. Complete the two-column proof.
Given:
Prove:
Drawing not to scale
Given
Substitution
Vertical
Substitution
34. Write the two conditional statements that form the given biconditional.
Three points are collinear if and only if they are coplanar.
If 3 points are collinear, then they are coplanar.
If 3 points are coplanar, then they are collinear.