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Transcript
Honors Geometry Chapter 2 Review
Name __________________________________
SHOW ALL WORK FOR FULL CREDIT!!!
1.) Sketch the next figure in the pattern.
2.) Describe the pattern AND write the next 3 numbers in the pattern.
a.) –5, 7, –9, 11, –13,…
d.)
1 3  5 7
, ,
, , ...
2 3 4 5
b.) 5.1, –6.2, 7.3, –8.4, …
c.) 100, 101, 98, 103, 96, …
e.) –1, 1, 5, 13, 29,…
f.) 1.1, 3.3, 13.2, 66, 396,…
3.) Show the conjecture is false by finding a counterexample.
a.) The sum of the squares of any two consecutive squared whole numbers is an even number.
b.) The sum of the squares of any two squared whole numbers is an odd number.
4.) For the given ordered pairs, write a function rule relating x and y.
a.) (1,–3), (2,–4), (3,–5), (4,–6)
b.) (1, 4), (2, 9), (3, 16), (4, 25)
5.) For the given statement, write the conditional in if-then form, the converse, the inverse,
and the contrapositive. Then mark if each is True or False.
“The sum of two supplementary angles is 180°.”
Conditional: __________________________________________________________________
True
____
False
____
Converse: ____________________________________________________________________
____
____
Inverse: ______________________________________________________________________
____
____
Contrapositive: ________________________________________________________________
____ ____
6.) For the given statement, write the conditional in if-then form, the converse, the inverse,
and the contrapositive. Then mark if each is True or False.
“A circle with a radius of r has a circumference of 2r.”
Conditional: __________________________________________________________________
True
____
False
____
Converse: ____________________________________________________________________
____
____
Inverse: ______________________________________________________________________
____
____
Contrapositive: ________________________________________________________________
____ ____
7.) Rewrite the definition as a biconditional statement.
a.) A conditional statement is a logical statement that has two parts, a hypothesis and a conclusion.
b.) A counterexample is a specific case for which a given conjecture is false.
In 8-11, a.) Use deductive reasoning along with one of the laws of logic to write the statement that
follows from the given statements.
b.) Indicate whether the Law of Detachment or the Law of Syllogism used
8.) If you park a car on a hill, then you should set the parking brake.
You park the car facing down a steep grade on a busy street.
9.) If you take the absolute value of a positive number, then the value of the result is the number.
You take the absolute value of a perfect square.
10.) If the ice on a lake becomes brittle, it may not be safe to walk on the ice for up to 24 hours.
If there is a large, rapid decrease in air temperature, then the lake ice becomes brittle.
11.) If an object has a greater volume than an equivalent mass of water, then the object will float in water.
A ball has three times the volume of an equivalent mass of water.
9.) Decide whether inductive or deductive reasoning is used to reach the conclusion.
Explain your reasoning.
a.) You use the rise of 8.1 and the run of 2.7 between two points on a line in the coordinate plane to
conclude that the slope of the line is 3.
b.) It is the last day of the month and you want to buy a new jacket. Because you always run out of money
by the end of the month, you conclude that there is not enough money in your checking account for the
jacket.
10.) Use the diagram to write an example of the given postulate.
a.) Postulate 5
b.) Postulate 6
c.) Postulate 7
d.) Postulate 8
e.) Postulate 9
f.) Postulate 10
g.) Postulate 11
11.) Can the statement be assumed to be true from the diagram? Explain.
a.) AB and AD are opposite rays.
b.) BAC and CAD are supplementary.
c.) BAC  BAE
d.) CE  plane S
e.) BD lies in plane S and in plane T
f.) If G is a point in plane S, then CG lies in S.
g.) CE bisects BD
h.) Plane T bisects BD
.
12.) Solve the equation. Write a reason for each step.
a.) 6(7x + 18) = (x + 8)4
b.) –11(x + 3) + (3x + 16) + 18 = (8 – 3x) 7
13.) Use the property to complete the statement.
a.) Transitive Property of Equality: If a = bc and bc = de, then ___________________________________.
b.) Substitution Property of Equality: If x = 3c and r = 5x + 7, then ________________________________.
14.) GIVEN: AB  BC , BC  CD , CD  AD
PROVE: Perimeter of ABCD = 4AB
Statements
Reasons
1. AB  BC , BC  CD , CD  AD
1. ______________________________________
2.
AB = BC, BC = CD, CD = AD
2. ______________________________________
3.
AB = CD, AB = AD
3. ______________________________________
4.
Perimeter of ABCD = AB + BC + CD + AD
4. ______________________________________
5.
____________________________________
5. Substitution Property of Equality
6. ____________________________________
6. Simplify.
15.) GIVEN: AE  CE ; AB and CD bisect each other.
PROVE: EB  ED
Statements
Reasons
1. AE  CE ; AB and CD bisect each other
1. ______________________________________
2. E is the midpoint of AB and CD
3. ______________________________________
3. EB  EA and EC  ED
3. ______________________________________
4. EA ED
4. ______________________________________
5. EB  ED
5. ______________________________________
16.) Find the values of the variables.
a.)
b.)
c.)
d.)