Name: ________________________________Period: ______________
0.1 Lines & Segments
Use the diagram to answer questions 1- 5
1) Name 1 set of three collinear points ________
A
nd
2) Name a 2 pair of points which are collinear _________
B
F
3) Name 1 pair of opposite rays. ______ and ______
C
The must have a common endpoint.
D
E
A
4) Name 2 lines that appear to be parallel ______ and _______
A
5) Name 3 points that are non-collinear. _____ _____ _____
Use the diagram to answer questions 6 – 13
The two planes shown, Plane PQR, and Plane SUV intersect.
6) What object lies at the intersection of the two planes? _______
7) Does ⃗⃗⃗⃗⃗
𝑈𝑉 contain ̅̅̅̅
𝑇𝑈? _______
8) Does ̅̅̅̅
𝑄𝑆 lie on plane PQR? _______
9) List all points on plane RSV. ______________
10) What is another way to name plane RSV?
_______
⃡⃗⃗⃗⃗ and 𝑈𝑉
⃡⃗⃗⃗⃗ ?
11) What object lies at the intersection of 𝑅𝑇
12) Name a point that is non-coplanar to points S,U, and V.
13) Name two opposite rays
_______ and _______
_______
_______
Use the map of the University of Arizona Campus to find the indicated examples
14) Find 3 examples of “points” – Consider places that may interest you.
15) Find 3 examples of “line segments.” Describe them as line segments that have a beginning
point and an end point.
16) Find 2 examples of points formed by the intersections of lines. Describe the points by what
is intersecting.
17) Find 2 examples of lines segments which appear to never intersect.
18) Why do these streets represent line segments and not lines?
Name: ___________________________________ Period: ________
0.2 Pool tables and planes
Pool tables & Planes
Pool Table Standard 8 ball game
Rack of a standard 8 ball game
Image: dreamstime.com
(image: acclaimImages.com)
In a standard 8 ball game, the balls are placed in a triangular rack on the pool table.
1) Which of the pool balls are coplanar with the 8 ball? What plane are they on?
2) In the image of the rack of a standard 8 ball game, name at least three different sets of pool balls which
are collinear with the 8-ball. How would you describe them?
3) After the balls are scattered with a break shot,
a) Are the balls still coplanar? Yes/no and why:
b) Which pool balls are still collinear to the 8-ball? Explain
c) Describe a scenario when at least one of the pool balls are NOT coplanar with the 8-ball.
Be creative.
4 a) On the diagram of the rack of the 8-ball game, draw a ray that starts with the 5 ball and goes through
the 13 ball.
b) Draw the opposite ray that starts with the 5. What other numbers does the ray go through? _____
c) What do the opposite rays form? ___________
d) Draw a third ray that starts with 5 but is not an opposite ray. What other numbers does the ray go
through? _____
e) What do rays that are not opposite rays form?
5)
a) Name a set of three points that are collinear ____ ____ ____
b) Name a set of three points that are NOT collinear
____ ____ ____
c) Name a set four points that are coplanar ____ ____ ____ ____
d) Name a set four points that are NOT coplanar ____ ____ ____ ____
e) Name a pair of opposite rays _________ and _________
6)
Plane M
a) Which line intersects both planes? ____________
Name the same line but in a different way ____________
H
Plane P
b) What is another way to name plane P? ___________
Name plane M in another way. ___________
c) Are points B and F collinear? _______ explain
d) Are points A, B, C collinear? _______ explain
e) Are points D, E, F coplanar? _______ explain
f) Are points A, B, C, D coplanar? _______ explain
Remember lines are named with only two points and use the symbol for the line above the points.
Rays are named with two points, the first point is the end point and the arrow always goes to the right.
Planes are named with three points and NO symbol is used.
Name: ________________________________Period: _________
0.3 Segment Addition Assignment
1. Find HJ
2. A) Find the value of 𝑥 if 𝐴𝐵 = 19
B) What is the length of 𝐴𝐵 − 𝐶𝐵?
3. What is the length of 𝑀𝑁?
4. Kyle is traveling to meet some friends for a hike. His friends told
him to they would all meet at the trail head which is half way
between Greenville and St. Louis. He sees this road sign while
driving toward the trailhead.
How far is it from his current location to the trailhead?
5. It’s Friday night, and the football team is readying a forward
pass. The quarter back throws the ball from his team’s 15
yard line, where his receiver catches it at his own 47 yard
line (he hasn’t crossed the 50 yard line yet). The receiver
runs and is tackled halfway between the 50 yard line and the
end zone at the other end of the field.
a) For how many yards was the ball in the air?
Ball Thrown from
here, to the right.
b) How many total yards did the team gain on this play? (include running yards)
6. What is the value of x?
7. U is the midpoint of 𝑇𝑉. Find the length of 𝑇𝑉.
8. Determine the length of 𝑃𝑄.
9. In the table shown below, are the distances between each of the 10 hurdles in men’s and women’s races.
Event
Race Length
Distance from
Start to 1st hurdle
Distance between
hurdles
Men’s
Women’s
110 m
100 m
13.72 m
13.00 m
9.14 m
8.50 m
Distance from the
last hurdle to the
finish
?
?
a) What is the distance between the last hurdle and the
finish line for the men’s race? Show your work.
b) What is the distance between the last hurdle and the finish line for the women’s race? Show your work.
Name: ___________________________________ Period: ________
0.4 Hand Measurement Activity
Hand Measurement Activity
1) Place the base of one palm on the P below. Keep your fingers within this page.
2) Spread your fingers apart and lightly trace around each finger.
You will write over these words.
3) Draw a point at the end of each finger and label the points with capital letters
T (thumb)
I (index)
M (middle)
R (ring)
B (baby).
4) Using a straight edge, draw five rays that each begin at the palm, point P, and continue through the points
⃗⃗⃗⃗⃗ , ⃗⃗⃗⃗⃗
at the end of each finger. You should have five rays ⃗⃗⃗⃗⃗
𝑃𝑇, ⃗⃗⃗⃗
𝑃𝐼 , ⃗⃗⃗⃗⃗⃗
𝑃𝑀, 𝑃𝑅
𝑃𝐵
5) Using a protractor, measure ∠BPR ___________ ∠RPM___________ ∠MPI__________ ∠IPT___________
6) Name the angle that goes between ring finger, palm and index finger. ____________, measure it __________
Name the two smaller adjacent angles that make up the angle you just measured _______ and ________.
What do each of those angles measure? _________ and __________. What is their sum? _________
Write two equations, one with symbols and one with numbers, that describe this angle addition.
Numbers:____________________________________ symbols: _________________________________
7)
What is the numeric sum of all 4 angles from question 5? ________ Name the angle they create _________
Use your diagram to measure that angle ____________. Are your answers the same? Explain any differences.
Image: simplebodylanguage.com
.
Draw an angle with the given measurement. Use segment provided.
Name: __________________________________ Period: ________
0.5 Ample Angle Activities
Ample Angle Activities
1) The angle below is an obtuse angle. There are at least 19 ways to name this angle. List them:
J
K
L
P
O
N
M
C
Angle Adjectives
A
B
2a) Measure ∠ABC to the nearest degree __________
b) What kind of angle is ∠ABC?
__________
c) Carefully bisect ∠ABC. Show all construction marks.
⃗⃗⃗⃗⃗
Place point P on the ray that bisects ∠ABC, draw 𝐵𝑃
d) Measure ∠CBP ___________ and ∠ABP __________.
What kind of angles are they? ________________________________
Some words that
describe angles include:
Acute
Obtuse
Right
Straight
Adjacent
Congruent
R
T
3a) Measure ∠RST to the nearest degree __________
b) What kind of angle is ∠RST?
__________
c) Carefully bisect ∠RST. Show all construction marks. Place point P on the ray that bisects ∠RST
⃗⃗⃗⃗ (you will draw into these words)
draw 𝑆𝑃
d) Measure ∠RSP ___________ and ∠TSP __________. What kind of angles are they?
e) In symbols: ∠RSP + ∠TSP = ______
f) Using your measurements does ∠RSP + ∠PST = ∠RST? Why or why not?
4a) Measure ∠CAT to the nearest degree __________
b) What kind of angle is ∠CAT?
__________
c) Carefully bisect ∠CAT. Show all construction marks. Place point K on the ray that bisects ∠CAT.
d) Measure ∠CAK ___________ and ∠KAT __________. What kind of angles are they? List at least
three ways as you can to describe these angles
____________ _________________ ______________.
C
A
T
Name: __________________________________ Period: ________
0.6 Angle & Segment Addition
Name:_______________________________________ Period:______
0.7 Review for Quiz 1
Using the diagram at right: Find examples of the following.
1: Three collinear points
2: Two opposite rays
●E
3: Two intersecting lines
4: The intersection of plane A1AD and plane A1B1C1
M is the midpoint of ̅̅̅̅
𝐴𝐵. Given that 𝐴𝑀 = 4𝑥 − 3 and 𝑀𝐵 = 2𝑥 + 17. Solve for x, then find the lengths
of
x = ______
5: ̅̅̅̅̅
𝐴𝑀
A
M
6: ̅̅̅̅̅
𝑀𝐵
̅̅̅̅
7: 𝐴𝐵
8. Segment addition
A)
x = ________
How long is 𝑆𝑉? ______
B) How long is ⃗⃗⃗⃗⃗⃗
𝑇𝑈 ?
B
9. What kind of angles are ∠1 and ∠2?
____________________________
⃗⃗⃗⃗⃗ 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝐴𝐵𝐷, 𝑎𝑛𝑑 ∠1 = (3𝑥 − (−4))°𝑎𝑛𝑑 ∠2 = (8 − 𝑥)°, 𝑠𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑥
10. If 𝐵𝐶
11: Using your value of 𝑥, write the measurement of each angle in the diagram above. Remember what it
means to bisect.
𝑚∠1 = ______________
𝑚 ∠2 = ______________
12. If your drawer of socks was full of unmatched socks and you had 10 red socks, 12 purple socks, and
14 white socks, how many would you have to pull out to guarantee you have a matching pair?
Part 2 will involve constructions. You should practice each of the following:
1) Label the angle ∠MNR. 2) Measure ∠MNR = __________ 3) Bisect ∠MNR show all construction
marks. 4) Use your tools to draw an angle that measures 40ᵒ. Label the new angle ∠𝑇𝑈𝑉.
5) Create the perpendicular bisector of segment AB Use
protractor and show construction marks.