Download Ch. 2 Study Guide

Geometry Chapter 2 Review
Must complete
before test.
1. Logical Statements:
a. If you are 14 years old then you are a teenager.
Hypothesis:
Conclusion:
Converse:
Counterexample:
Name: ____________________________
b. Odd integers are not divisible by 2.
Conditional:
Converse:
Contrapositive:
Can a true biconditional be formed in this case? If so
write it. If not explain why not.
Contrapositive:
Can a true biconditional be formed in this case? If c.
so write it. If not explain why not.
Amphibians
Frogs
Euler Diagram:
Conditional:
Contrapositive:
Ben is a teenager. Deduction (if possible):
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.
This statement forms a logical chain when
the statements are in this order:
___ ___ ___ ___
Conditional that follows from this logical
chain:
d) If you live where it is cold, you need a warm coat.
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.
Conditional:
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: ___ ___ ___ ___
Conditional:
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: ___ ___ ___
Conditional:
Does “If not y then not p” have to be true?
Why?
3.
Inductive reasoning
Inductive reasoning is the process of arriving at a
conclusion based on a set of observations. In itself, it
is not a valid method of proof.
Deductive reasoning
Deductive reasoning is a valid form of proof. It is the
way in which geometric proofs are written. Deductive
reasoning is the process by which a person makes
conclusions based on previously known facts.
In geometry, inductive reasoning can helps us
organize what we observe so that we can prove
theorems by using deductive reasoning.
b. Angela draws 5 triangles and measures all the
angles in each. She observes that the sum of the
angles in each triangle is 180°. Therefore, the sum
of the angles in all triangles must be 180°.
_______________________
c. Angles that are less than 90° are acute. ABC =
30°, therefore ABC is acute. ________________
d. Every time John eats strawberries, he breaks out in
hives. Therefore John is allergic to strawberries.
____________________
Identify each as inductive or deductive reasoning.
e. If I sleep until 8 am then I am well-rested. If I am
well-rested then I like to go running. Saturdays I
a. The Pirates have won their last 3 home games.
sleep until 8 am. Therefore, I like to run on
Therefore the Pirates will win their next home
Saturdays. ____________________
game. __________________
4. The following are questions from the CST geometry test. There may be questions similar to these on your
test. Make sure you understand them.
a.
b.
c.
d.
e.
f.
5. 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
6. For each problem a – e, fill in the correct type of angles form 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
7. 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)°
e.
f.
(4x + 1)°
2
8. Solve for x and justify each step.
* You will be able to
use your definitions,
postulates and
theorems 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
9. Given: 1and 2 are vertical; 2  3 .
Prove: 1  3
O
1
Statements
Reasons
1and 2 are vertical
given
Vertical Angle Theorem
2  3
A
V
2
E
3
given
10.
See your notes. We
did a similar proof
together in class.
Statements
Reasons
L
You must know all of the following constructions for your test. If you need more practice create your own
segments and angles and do each construction many times.
11. Perpendicular bisector of the segment.
12. Perpendicular through point on line
13. Perpendicular through point off line
14. Angle Bisector
15. Duplicate an Angle in the box to the right.
The duplicated angle must be the same size and shape,
but it does not need to orientated the same direction.
16. Duplicating Segments
A
B
Construct GH such that GH = AB:
Construct IJ such that IJ = AB + 2(EF):
Construct KL such that KL = 2(AB) – CD:
C
D
E
F
17. Construct the Incenter, the radius for the Incircle, and the Incircle:
18. Construct the Circumcenter and Circumcircle.
Algebra Review: The only algebra review on your test will be of the following type.
Find the equation of the line through:
Solve: 10 x  3( x  10)  6  6( x  5)
(8,11) and (12, 4) Must show an algebraic method.