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Geometry HW 2-6 Chapter 2 Review
Name: ____________________________ 9/29/2014
1. Logical Statements:
a. If you are 14 years old then you are a teenager.
Hypothesis:
Conclusion:
b. Odd integers are not divisible by 2.
Conditional:
Converse:
Converse:
Counterexample:
Can a true biconditional be formed in this case? If so
write it. If not explain why not.
Can a true biconditional be formed in this case? If c.
so write it. If not explain why not.
Amphibians
Frogs
Euler Diagram:
Conditional:
Inverse:
Ben is a teenager. Deduction (if possible):
Contrapositive:
Lindsay’s pet is a frog. Deduction (if possible):
2. Logical Chain.
a) If you live in the Antarctic, you live where it is cold.
b) If you live at the South Pole, you live in the Antarctic.
c) If you need a warm coat, then you need warm socks.
d) If you live where it is cold, you need a warm coat.
This statement forms a logical chain when
the statements are in this order:
___ ___ ___ ___
Deduction that follows from this logical
chain:
a) If the field is wet, the Pirates will not play baseball.
This statement forms a logical chain when
b) If the Pirates do not play baseball, Nathan can stop at the the statements are in this order:
Scoop after school.
___ ___ ___
c) If it rains a lot, the field is wet.
Deduction:
a)
b)
c)
d)
If Kate studies well, she will get good grades.
If Kate lives in the dorms, she will have fun.
If Kate goes to college, she will live in the dorms.
If Kate gets good grades, she will go to college.
This statement forms a logical chain when the
statements are in this order: ___ ___ ___ ___
Deduction:
a) If p then w.
b) If r then y.
c) If w then r.
This statement forms a logical chain when
the statements are in this order: ___ ___ ___
Deduction:
3. Name the definition, postulate or theorem that justifies each step. You can use your definitions, postulates
and theorems handout on this question.
a. If UV  KL and KL  6 then UV  6
b. If m1  m2  90 then 1 and 2 are
complementary.
c. If m1  90 then 1 is a right angle.
d. If 1 and 2 are vertical angles then 1  2 .
e. RS  TW , then TW  RS
f. If 5 y  30 , then y  6
4. For each problem a – e, fill in the correct type of angles from the list of choices. Use each answer once.
a.
b.
Choices: 1 and 2 are…
Vertical Angles
1
2
1
A Linear Pair
2
Complementary and Adjacent
Complementary not Adjacent
Supplementary not Adjacent
e.
c. m1  60 and m2  120
d. m1  60 and m2  30
1
2
1
1
2
5. Solve for x and find the measure of all angles in each diagram.
a.
b.
(3x + 32)°
(8x – 11)°
(2x +13)°
c.
(x + 20)°
d.
(7x – 9)°
(x + 7)°
(2x)°
(4x – 5)°
(4x + 1)°
2
e.
f.
6. Solve for x and justify each step.
* You will be able to
use your beige sheet
on this type of
question on the test.
M
(9x – 14)°
Given: NA bisects MND
Prove: x  17
N
Statements
Reasons
(6x + 37)°
D
N
7. Given: 1and 2 are vertical; 2  3 .
Prove: 1  3
O
1
Statements
Reasons
1and 2 are vertical 2  3
given
Vertical Angle Theorem
8. Algebra Review:
a. Solve: 10 x  3( x  10)  6  6( x  5)
A
V
2
E
b. Find the equation of the line through:
(8,11) and (12, 4)
3
L
ANSWERS:
1a. hyp: you are 14. Concl: you are a teenager. Conv: If you are a teenager, then you’re 14 years old.
Counterexample: you could be 15. No biconditional because the conditional and converse must both be true to
write a biconditional. Diagram: teenagers outside, 14yr olds inside. No deduction possible.
b. Cond: if an integer is odd, then it is not divisible by 2. Converse: If a number is not divisible by 2, then it is
an odd number. Biconditional: A n umber is odd iff it is not divisible by 2.
c. If something is a frog, then it is an amphibian. Inverse: If something is not a frog, then it is not an amphibian.
Lindsay’s pet is an amphibian. Contrapositive: If something is not an amphibian, then it is not a frog.
2. BADC, If you live at the south pole, then you need warm socks. CAB, if it rains a lot, then Nathan can stop
at the scoop after school. ADCB, If Kate studies well, then she will have fun. ACB, if p, then y.
3. a. transitive property of equality. B. definition of complementary. C. definition of right angle. D. definition of
vertical angles. E. reflexive property of congruence. F. division property of equality.
4. a. Complementary and adjacent. B. vertical. C. supplementary not adjacent. D. complementary not adjacent.
E. linear pair
5. a x = 4, both 21 degrees
d. x=14, 51, 51, 57, 21
b. x =32, 128 and 52 degrees.
e. x=14, y=15, 50 and 130 degrees
C. x=11, 68 and 22 degrees.
f. x=35, y=70, 110 degrees
6. NA bisectos angle MND – given
Angle MNA is congruent to angle AND – definition of bisect
9x-14 = 6x +37 – substitution
3x-14 = 37 – subtraction property of equality
3x = 51 – addition prop of equality
X = 17 - division prop of equality
8. Angle 1 is congruent to angle 2
Angle 1 is congruent to angle 3 – transitive property of congruence
9. x= - 6 , y=(-3/4)x+5
You may use your green sheet notes
and beige sheet of postulates and
definitions for the test- but no other
notes, no calculator and no
headphones! I’ll look at your binders
and update your HW scores while
you’re doing the test, so make sure
you have all of HW from Ch 2 done.
No HW from Ch 2 will be given credit
after the test day. Work hard!