Download Chapter 1 Study Guide

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Chapter 1 Study Guide
1. Find two counterexamples to prove the conjecture is false.
Conjecture: Any number that is divisible by 6 is also divisible by 12.
2. Make a conjecture about the relationship between three consecutive whole numbers based on this relationship
illustrated by the numbers 7, 8, and 9:
. Can you find a counterexample?
3. Based on the pattern, make a conjecture about the sum of the first 15 positive even numbers.
2
=
2 =
2+4
=
6 =
2+4+6
= 12 =
2+4+6+8
= 20 =
2 + 4 + 6 + 8 + 10
= 30 =
4. Alfred is practicing typing. The first time he tested himself, he could type 34 words per minute. After practicing
for a week, he could type 40 words per minute. After two weeks he could type 46 words per minute. Based on this
pattern, predict how fast Alfred will be able to type after 4 weeks of practice.
5. Name plane shown in the diagram. State the postulate that supports your answer.
T
U
R
S
Use the figure below for problems 6 and 7.
6. What is the intersection of plane WZVS and plane STUV? State the postulate that supports your answer.
7. What it the intersection of WZ and ZY ? State the postulate that supports your answer.
8. Name the ray that is opposite
D
C
B
A
9. Name four different rays shown.
V
X Y
Z
Use the figure below for problems 10 and 11.
10. Name the four labeled segments that are skew to
11. Name three segments parallel to
12. If
find the values of x, EF, and FG. The drawing is not to scale. Use a
postulate, property, or definition to justify your reasoning.
E
F
G
13. If T is the midpoint of
find the values of x and ST. The diagram is not to scale. Use a postulate, property, or
definition to justify your reasoning.
S
T
5x
14.
U
2x + 15
bisects
and
Solve for x and find
is not to scale. Use a postulate, property, or definition to justify your reasoning.
The diagram
15.
and
are complementary angles. m
=
, and m
angle. Use a postulate, property, or definition to justify your reasoning.
Name an angle or angles in the diagram described by each of the following.
16. supplementary to
17. complementary to
18. congruent to
19. a pair of vertical angles
Use the figure below for problems 20 – 23.
20.
21.
22.
23.
=
. Find the measure of each
24. Find the measure of each angle. Use a postulate, property, or definition to justify your reasoning.
25. Find the distance between points P(5, 5) and Q(6, 8). Leave your answer in simplest radical form.
26. M(3, 6) is the midpoint of
The coordinates of S are (5, 8). What are the coordinates of R?
27. A map of a city and suburbs show an airport located at A(25, 11). An ambulance is on a straight expressway
headed from the airport to Grant Hospital at G(1, 1). The ambulance gets a flat tire at the midpoint M of AG . As
a result, the ambulance crew calls for helicopter assistance.
a. What are the coordinates of point M.
b. How far does the helicopter have to fly to get from M to G? Assume all coordinates are in miles.