Do Now 4 – Points, Lines, and...

Geometry

Level 2 Ms. Sheppard-Brick

Do Now 4 Name: Date:

Do Now 4 – Points, Lines, and Planes

Directions: Use the figure at the right to decide whether the statement is true or false.

1. C lies on line d.

2. X, Y, and Z are collinear.

3. A is a plane.

4. 𝐶𝑌 is a line.

Directions: Use the figure at right to answer the following questions.

5. Name the points on plane S.

6. Name two lines.

7. Name the plane that contains point D.

8. Name three collinear points.

9. Decide whether the following statement is true or false: Points K, F, and F are coplanar.

Geometry Week 2 Packet

Geometry Level 2

Ms. Sheppard-Brick 617-596-4133

Intersections – Notes Name: Date:

Intersections – Guided Notes and Investigation

Investigation

Group Roles

List the names of the person in your group who is filling each group role.

Facilitator ___________________ Reader __________________________

Materials Manager __________________ Recorder ______________________

Materials:

• 2 pencils

• 3 index cards

• 1 pair of scissors

Instructions

The pencils will represent lines and the index cards will represent planes. Because planes are flat, you should not bend or fold the index cards when you are using them as a model. You may want to cut them though.

1. Model the intersection of two lines with your pencils. Determine whether two lines can meet: one time, two times, an infinite number of times. Draw a sketch of any intersections that are possible.

Can two lines intersect once? Can two lines intersect exactly

twice? Can two lines intersect an infinite number of times?

Yes or No (circle one) Yes or No (circle one) Yes or No (circle one)

If yes, sketch the intersection. If yes, sketch the intersection. If yes, sketch the intersection.


Geometry Level 2



2. Model the intersection of two planes using the index cards. Determine whether two

planes can intersect: one time, two times, and infinite number of times. (Hint, cut your index cards as shown below to make them intersect.)

Can two planes intersect once? Can two planes intersect

exactly twice? Can two planes intersect an infinite number of times?



3. Model the intersection of a line and a plane using one pencil and one index card. Determine whether a line and a plane can intersect: one time, two times, and infinite number of times. You may need to poke a hole in your plane to find some intersections.

Can a line and a plane intersect once?

Can a line and a plane intersect exactly twice?

Can a line and a plane intersect an infinite number of

times?



Intersecting Planes with Index Cards:

Cut each index card where the dotted line is. Fit one index card into the other.


Geometry Level 2



Formalize

If two lines intersect once, they intersect at a _________________.

If two lines intersect an infinite number of times, they intersect at a ______________.

If two planes intersect once, they intersect at a ________________.

If two planes intersect an infinite number of times, they intersect at a ___________.

If a line and a plane intersect once, they intersect at a ________________.

If a line and a plane intersect an infinite number of times, they intersect at a ___________.

Practice


Geometry Level 2



Directions: Sketch the figure described.

8. Sketch a plane and a line that intersects the plane. Then sketch a line in the plane that intersects the first line.

9. Sketch a plane and a line that intersects the plane. Then sketch another line that intersects the plane and does not intersect the first line.

10. Sketch two planes that intersect in a line. Then sketch a line that intersects each of the planes, but does not intersect the first line.


Geometry Level 2

Homework 5 Name: Date:

Homework 5 – Sketching Intersections

Directions: For each of the following problems, name the intersection, or write ‘no intersection.’

1) The intersection of .



4) The intersection of Y and Z.

5) The intersection of W and Y.

6) The intersection of X and Z.

Directions: Sketch each of the figures described.

7) Three lines that lie in a plane and intersect in a point

8) Three planes that do not intersect

9) Two lines in a plane that do not intersect

10) A line that intersects a plane at a point

Directions: for problem 11, show your work and/or explain how you got your answer for each

part of the problem.

11) Briana is finding real world examples for geometric intersections. She thinks that two

railroad tracks might represent lines and the switch (where they meet) would represent the

point of intersection.

a) Give another real world example of two lines and their intersection. Be sure to explain what

represent the lines and what represents the intersection.

b) Give a real world example of figures that represent two planes and their intersection. Be sure

to explain what represent the planes and what represents the intersection.

c) Give a real world example of figures that represent two coplanar lines that do not intersect. Be

sure to example what represents the plane and what represents the lines.


Geometry Level 2


Do Now 5 Name: Date:

Do Now 5 – Solving Equations Practice

Directions: Solve the following equations for the variable. Show your work.

1. 5x – 3 = 2

2. 3n + 2 = 17


Math 2: Algebra 2, Geometry and Statistics

Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434

Segments & Measures Name: Date:

Segments and Their Measures – Guided Notes

Vocabulary Coordinate – the real number that corresponds to a ______________________. Distance (aka length of a segment) Definition:

Notation

Figure Example(s):

Example 1: measure the length of each segment in centimeters. Round to the nearest tenth. a. b. Between – Definition:

Notation

Figure Example(s):





Segment Addition Postulate: If point B is between points A and C, then AC = AB + BC If:

Then:

Converse of the Segment Addition Postulate: If AC = AB + AC, then point B is between points A and C. If:

Then:

Example 2: Find the length of the segment indicated. a. Find AC

b. Find DE

Congruent Segments – Definition:

Notation

Figure Example(s):

yx

A CB

x + y

A CB

x + y

A CB

yx

A CB





Example 3: Determine whether the segments are congruent.

Example 4: Draw a sketch of the three collinear points. Then write the Segment Addition Postulate for the points. a. E is between D and F b. H is between G and J

c. M is between N and P d. R is between Q and S





A

C

H

G

E

F

B

D

Practice Directions: Use the diagram to determine whether the statement is true or false.

1. B is between A and C.

2. E is between C and F.

3. E is between D and H.

4. D is between A and H.

5. C is between B and E. Directions: Find the length of the given segment.

6. Find PR

7. Find SU

8. Find MN

9. Find JK

Directions: Determine which segments in the coordinate plane are congruent. 10.

7 cm9 cmP RQ 16 cm5 cmS UT

21 cm

11 cmL N

M

23 cm

17 cmJ L

K

4

2

–2

–4

–6

–5 5

A

B

C D

F

G H

E


Geometry Level 2


C

A B

D

Homework 6 – Segments and Their Measures

Directions: Use a ruler to find the length of each segment. Measure in centimeters and round to the nearest tenth of a cm.

Directions: Use the segment addition postulate to find the length of each segment. All measurements are in centimeters.

5.

6.

7.

8.

Directions: Write an algebraic expression for the length of each segment.

9. Write an expression for EG (the length of segment EG.)

10. Write an expression for LM (the length of segment LM.)

Directions: for problem 11, show your work and/or explain how you got your answer for each part of the problem.

11. The rectangle shown below is a scale model of Elizabeth’s room where 1 cm = 1 m (1 centimeter on the diagram is equal to 1 meter in the room.)

a. Find the length of AB to the nearest tenth of a centimeter.

b. What is the length of Elizabeth’s bedroom (represented by AB?)

c. Find the length of AD to the nearest tenth of a centimeter.

d. What is the width of Elizabeth’s bedroom (represented by AD?)

e. What is the area of Elizabeth’s bedroom in square meters?




Angles & Measures Name: Date:

Angles and Their Measures – Guided Notes and Practice

Vocabulary Angle – Definition:

Notation

Figure Example(s):

Sides of an Angle – Definition:

Notation

Figure Example(s):

Vertex of an Angle – Definition:

Notation

Figure Example(s):

Measure of an Angle – Geometry Week 2 Packet




Definition:

Notation

Figure Example(s):

Measuring an Angle

1. Place the center of the protractor over the vertex of the angle. 2. Align the protractor with one side of the angle. 3. Read where the second side of the angle crosses the protractor.

Example 1: Name each angle and measure each angle to the nearest degree. a.

b.

c.

d.

Classifying Angles

B C

A

D F

E

I

G

HK

J

L





Angles with a measure between 0° and 90°.

Angles with a measure between 90° and 180°.

Angles with a measure of 90°.

Angles with a measure of 180°.

Example 2: Classify each angle.

a. m∠𝐴 = 130°

b. m∠𝐵 = 90°

c. m∠𝐶 = 45°

Angle Addition Postulate If P is in the interior of ∠𝑅𝑆𝑇, then the measure of ∠𝑅𝑆𝑇 is the sum of the measures of ∠𝑅𝑆𝑃 𝑎𝑛𝑑 ∠𝑃𝑆𝑇. If:

Then:

Example 3: Find the measure of ABC. a. b. c.

y°

x°

S

R

T

P

(x + y)°

S

R

T

P





Practice Directions: Name the vertex and sides of each angle. Then name the angle in two ways 1.

2.

3.

Vertex: Sides: Angle Names:



Directions: Measure each angle to the nearest degree, then classify the angle. 4.

5.

6.

Measure: Classify:

Measure: Classify:

Measure: Classify:

Directions: Find the measure of the angle. 7. m∠𝐷𝐸𝐹 = 8. m∠𝐺𝐸𝐹 = 9. m∠DEF =

20°60°

B

A

D

C

90°

40°

B

A D

C

90°

40°

B

A C

D

X

F

T

O

RS

N

K

E

X

F

T

O

RS

N

K

E





Directions: Plot the points on the coordinate plane. Then measure angle ABC and classify it. 10. A (3, 0), B (0, 0), and C (0, 3)

Measure: Classification:

11. A (3, 0), B (0, 0), and C (4, -‐4)


12. A (-‐3, 0), B (0, 0), and C (2, -‐2)


13. A (0, 4), B (0, 0), and C (2, 2)


60°

45°

E

D

G

F

60°

95°

E

D

G

F

160°60°

E

D

G

F

4

2

–2

–4

–5 5

4

2

–2

–4

–5 5

4

2

–2

–4

–5 5

4

2

–2

–4

–5 5


Geometry Level 2


54°

62°

G

F

C

D

A

B

E

Homework 7 – Angles and Their Measures

Directions: Use a protractor to measure the angle to the nearest degree. Then state whether the angle is acute, obtuse, right, or straight.

1.

2.

3.

Directions: Find the measure of the indicated angle.

4. Find m∠JKN

5. Find m∠𝐸𝐹𝐻

6. Find m∠𝑅𝑄𝑡

7. Find m∠𝑅𝐸𝑍

8. Find m∠𝑅𝑇𝑆

9. Find m∠GPS

Directions: for problem 10, show your work and/or explain how you got your answer for each part of the problem.

10. Anthony sketched the figure at right and measured some of the angles.

a. Find the measure of ∠𝐹𝐺𝐸. Show or explain how you got your answer.

b. Find the measure of ∠𝐴𝐺𝐹. Show or explain how you got your answer.

c. Find the measure of ∠𝐴𝐺𝐵. Show or explain how you got your answer.


Do Now 4 – Points, Lines, and...

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