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Review Supplement
Unit 01a: Proof, Parallel, Perpendicular Lines, Part 1 (SB Geom)
You will be able to identify, describe,
and name points, lines, line segments,
rays, and planes using correct notation
Purple Geometry Textbook P. 60: 1, 4-8
1.
Draw and carefully label plane FAR
⃡ .
that intersects plane RAP at 𝐴𝑅
2.
Let (4x + 8)° represent the measure
of an obtuse angle. What are the
possible values of x written as a
compound inequality?
3.
A and B are supplementary
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
You will be able to identify and name
angles
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
You will be able to describe angles and
angle pairs
Purple Geometry Textbook P. 60: 2; P. 62:
22-31
angles. Find the measures of the
angles when mA = (11x – 11)° and
mB = (3x2 – 5x + 2)°.
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
4.
Find the measure of each missing
angle.
5.
Find the value(s) of x.
(3x2+10x)°
42°
45°
(23x - 4)°
6.
Find the values of 𝑥 and 𝑦.
You will be able to identify and name
parts of circles
For the circle below, draw each of the
following line segments or lines.
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
C
⃡
Radius ̅̅̅̅
𝐶𝑃
10. Tangent 𝑇𝑃
Diameter
⃡
11. Secant 𝐹𝑃
̅̅̅̅̅
𝐹𝑊
9. Chord ̅̅̅̅̅
𝑃𝑊
12. Draw the next shape in the pattern
below.
7.
8.
You will be able to make conjectures by
applying inductive reasoning
Purple Geometry Textbook P. 134: 4; P.
138: 1-4
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
13. Find the first 13 terms in the
sequence below.
1, 1, 2, 3, 5, 8, …
Let fn be the nth term of the sequence
from Q13, where f1 = 1, f2 = 1, f3 = 2, etc.
If fn is the nth term, then fn+1 is the next
consecutive term. Mathematicians have
𝑓
found that the ratio 𝑛+1
approaches an
𝑓
𝑛
irrational number called the golden ratio.
15. Use a pattern to find the units digit
(the ones digit) of 7101. (To do this,
make a list of powers of 7 starting
with 70. Keep going until you
discover a pattern.)
14. Using your calculator and the
sequence from Q13, what number
𝑓
does the ratio 𝑛+1 approach?
𝑓𝑛
You will be able to recognize the limits
of inductive reasoning
Purple Geometry Textbook P. 134: 5
16. Explain the role of counterexamples
in mathematics.
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
For Q17-21, find a counterexample to
show the conjecture is false.
17. The square of any integer is a
positive integer.
18. The square root of a number 𝑥 is
always less than 𝑥.
19. The sum of the squares of any two
consecutive whole numbers is an odd
number.
20. All complementary angles form a
right angle.
21. Any three points are collinear.
You will be able to avoid fallacies of
inductive reasoning
22. It’s election time! This means
candidates from various parties are
running for a variety of offices
against an array of opponents. If
On a scale of 1-5, rate your confidence in
you’ve lived in this country for very
this objective (5 being the most
long, you know that these potential
confident):
politicians will say just about
anything to get elected, including
committing a number of inductive
fallacies to benefit their chosen
causes.
Explain how a politician might use a hasty generalization to gain the upper hand against their opposition.
(Make sure you study the other fallacies of inductive reasoning.)
You will be able to use deductive
reasoning to prove a conjecture is true
23. Explain the relationship between
inductive and deductive reasoning
in mathematics.
On a scale of 1-5, rate your confidence in
this objective (5 being the most
confident):
24. Use inductive reasoning to complete
the conjecture:
Conjecture: The product of any two
odd integers is ________________.
25. Use inductive reasoning to complete
the conjecture:
Conjecture: The average of any two
consecutive odd whole numbers is
_________________.
26. Use deductive reasoning to prove the conjecture you made in Q23.
27. Use deductive reasoning to prove the conjecture you made in Q24.
Use the following information on Q25Q26:
An even number is a multiple of 2, so
any even number can be represented by
2𝑘, where 𝑘 is an integer. Since an odd
number is just one more than an odd
number, any odd number can be
represented by 2𝑘 + 1.