Name: ________________________________Period: ______________ 0.1 Lines & Segments

Use the diagram to answer questions 1- 5

1) Name 1 set of three collinear points ________

2) Name a 2nd

pair of points which are collinear _________

3) Name 1 pair of opposite rays. ______ and ______

The must have a common endpoint.

4) Name 2 lines that appear to be parallel ______ and _______

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 𝑈𝑉⃗⃗ ⃗⃗ ⃗ contain 𝑇𝑈̅̅ ̅̅ ? _______

8) Does 𝑄𝑆̅̅̅̅ lie on plane PQR? _______

9) List all points on plane RSV. ______________

10) What is another way to name plane RSV? _______

11) What object lies at the intersection of 𝑅𝑇⃡⃗⃗⃗ ⃗ and 𝑈𝑉⃡⃗⃗⃗ ⃗? _______

12) Name a point that is non-coplanar to points S,U, and V. _______

13) Name two opposite rays _______ and _______

A

B

C

D E

A

A

F

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.

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.

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

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?

b) How many total yards did the team gain on this play? (include running yards)

Ball Thrown from

here, to the right.

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

Distance from the

last hurdle to the

finish

Men’s 110 m 13.72 m 9.14 m ?

Women’s 100 m 13.00 m 8.50 m ?

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 𝑃𝑇⃗⃗⃗⃗ ⃗, 𝑃𝐼⃗⃗⃗⃗ , 𝑃𝑀⃗⃗⃗⃗ ⃗⃗ , 𝑃𝑅⃗⃗⃗⃗ ⃗, 𝑃𝐵⃗⃗⃗⃗ ⃗

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

Angle Adjectives

Some words that

describe angles include:

Acute

Obtuse

Right

Straight

Adjacent

Congruent

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

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 𝐵𝑃⃗⃗⃗⃗ ⃗

d) Measure ∠CBP ___________ and ∠ABP __________.

What kind of angles are they? ________________________________

A

T

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

draw 𝑆𝑃⃗⃗ ⃗⃗ (you will draw into these words)

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

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 𝐴𝐵̅̅ ̅̅ . Given that 𝐴𝑀 = 4𝑥 − 3 and 𝑀𝐵 = 2𝑥 + 17. Solve for x, then find the lengths

of

x = ______

5: 𝐴𝑀̅̅̅̅̅ A M B

6: 𝑀𝐵̅̅̅̅̅

7: 𝐴𝐵̅̅ ̅̅

8. Segment addition

A) B) How long is 𝑇𝑈 ⃗⃗ ⃗⃗ ⃗⃗ ?

x = ________

How long is 𝑆𝑉? ______

9. What kind of angles are ∠1 and ∠2? ____________________________

10. If 𝐵𝐶⃗⃗⃗⃗ ⃗ 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝐴𝐵𝐷, 𝑎𝑛𝑑 ∠1 = (3𝑥 − (−4))°𝑎𝑛𝑑 ∠2 = (8 − 𝑥)°, 𝑠𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑥

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.