Show all work, even for any multiple-choice questions, so that your teacher can see .... In geometry class, you will learn to how to give proof that a mathematical ...

2019–2020 Summer Math Preparation for Student StudentsChange Who Will Take Geometry of Address Form What is the aim of this assignment? Doing this assignment will help you review math that you will need to know for your math course next year. It will you realize what topics you need to fix up before starting that course so Student help Name: ______________________________________________________________ _ that we can spend less time reviewing and more time learning new material. Printing: Please print this file out. Do your work right on the sheet. If you need sheets, you can work on the back or staple additional pages. Student additional Grade: _________________________________ Showing your work: You must work in pencil, not pen. Edit your mistakes and be neat. Parent/Guardian Name(s): ____________________________ ________________________________ Show all work, even for any multiple-choice questions, so that your teacher can see what you were thinking, give you feedback, and help you.

New Address: _______________________________________________________________ ______ Write your work clearly, so that someone else can follow your thinking. Use correct mathematics notation as well as English words.

City, State, ______ DueZip:______________________________________________________________ date: This assignment is due the first day of school. You have all summer to do this packet, but you really should start in July and work gradually so that you have time to do a great job. Home Phone Number: __________________________________________________________ _____ Grading: This assignment will be graded as part of your Quarter 1 grade. You may also be assessed on these topics in September. Getting Help: You are expected to work independently on this. You can ask classmates, Parent/Guardian cell phone number:___________________________________________________ _ friends, or others for suggestions, but you may NOT look at their written work. If someone asks you for help, don’t show them your work. Instead, guide them hints and ask questions that will help them.

I have read this description and agree to do this assignment independently.

Name

Date

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

2

Perfect Squares Fill in as many values as you can FROM memory. You do NOT need to go in order. The goal is to assess your memory, so if you don’t know a fact immediately, write a “?” — do NOT calculate!

122 =

302 =

182 =

192 =

152 =

72 =

132 =

252 =

202 =

142 =

162 =

62 =

112 =

212 =

172 =

102 =

1002=

302 =

242 =

92 =

When you are done, list the facts below that you did not know by heart below. Try to learn them before school starts in September.

In Grade 8, you studied the Pythagorean theorem. Explain it below with a simple diagram. Explain how knowing perfect squares by heart can make Pythagorean Theorem problems easier for you?

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

Solving Linear Equations Answer the following examples of linear equations. You need to show your work. Remember your work must be your own. 1) What is the solution of the equation? Justify each step with words.

w 2 3

2) Find the solution of the equation. Justify each step with words.

6 x 8 7 7

3) What is the solution of the equation? Justify each step.

17 13 8x

4) A square field has an area of 479 ft 2 . What is the approximate length of a side of the field? Give your answer to the nearest foot. Justify your answer.

3

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

4

5) A mountain climber ascends a mountain to its peak. The peak is 12,740 ft above sea level. The climber then descends 200 ft to meet a fellow climber. Find the climber’s elevation above sea level after meeting the other climber.

6) A camera manufacturer spends $2250 each day for overhead expenses plus $6 per camera for labor and materials. The cameras sell for $16 each. a. How many cameras must the company sell in one day to equal its daily costs?

b. If the manufacturer can increase production by 50 cameras per day, what would their daily profit be?

7) Some people say that there are three Pythagorean Theorems:

a2 + b2 = c2 b2 = c2 – a2 a2 = c2 – b2 Use your skills solving equations to explain why the second and third equation actually come from the first equation.

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

Solving Proportions Solve the proportion below as many ways as you can think of. You need to show at least four different ways. You can ask people for inspiration (but your work must be your own!) 𝑥 10 = 8 40 Example methods include: Using factors of change across the fractions. Using factors of change within the fractions Cross multiplying. Making patterns. Multiplying both sides by the same value Simplifying fractions first Trial and Error

5

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

Basic Terms Term

Description in words

3 Examples from the real world

(If you don’t remember, look up in a dictionary!)

Point

Line

Line Segment

Plane

Write a sentence distinguishing what acute, obtuse, and right angles. Include diagrams with your sentence to illustrate what you have said.

6

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

Triangles Make a list of every type of triangle you have ever studied. The last row is fully blank so that you can add the type of triangle missing from the list. Type

Description in words (If you don’t remember, look up in a dictionary)

Scalene

isosceles

All angles are less than 90°

One angle is 90°

One angle is greater than 90°

Drawing of an example

7

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

8

Quadrilaterals The diagram below is a family tree showing the relationship of different kinds of quadrilaterals. Some names and descriptions have been filled in to get you started. Fill in the rest. Quadrilateral

Kite

(two sides parallel, other two sides congruent)

Square

A square has a LOT of properties. Write a paragraph about them below, using a labeled diagram and the correct vocabulary, including words such as sides, angles, 90°, parallel, diagonals

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

Transversals In the diagram below, lines m and n are parallel.

m

n

1 2 3 4

5 6 7 8

Make a long list of complete sentences describing everything you see in the diagram above. Use words such as parallel lines, transversal, vertical angles, alternate interior angles, corresponding angles, alternate exterior angles , and interior angles on the same side of the transversal Use numerical relationships, such as congruent (equal) and supplementary. 1) Example: The angles 1 and 4 are vertical angles. They are congruent (equal). 2)

When you are done, write “NO” next to any sentence that is FALSE if m and n are NOT parallel.

9

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

10

Sequences of Patterns For each example find the sequence of patterns. You need to show and justify your answer for each example. You should work on each example on your own. 1) Bobby has a set of tiles similar to the ones shown below. He says that his tiles have a total of 9 red triangles. Is 9 a reasonable number of triangles?

Fig. 1

Fig. 2

Fig. 3

2) The table shows the relationship between the number of white triangles and the total number of square tiles in each figure. Complete the table and extend the pattern. What is the total number of white triangles in afigure with 6 tiles?

Fig. 1

Fig. 2 Number of Square Tiles (s) 1 2 3 4 5

Fig. 3 Number of White Triangles (t) 4

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

Proof In geometry class, you will learn to how to give proof that a mathematical statement is true. But the idea of proving something is true is not only part of mathematics — it’s part of life. Make a list of five situations in which someone must prove something. Situation In a real-life crime case

Who proved what?

How did they prove it?

In your own family life.

In a movie or TV show

In science

From your study of the bible

Look at the last column. What does proof always involve? Explain a couple of sentences.

11

New Address: _______________________________________________________________ ______ Write your work clearly, so that someone else can follow your thinking. Use correct mathematics notation as well as English words.

City, State, ______ DueZip:______________________________________________________________ date: This assignment is due the first day of school. You have all summer to do this packet, but you really should start in July and work gradually so that you have time to do a great job. Home Phone Number: __________________________________________________________ _____ Grading: This assignment will be graded as part of your Quarter 1 grade. You may also be assessed on these topics in September. Getting Help: You are expected to work independently on this. You can ask classmates, Parent/Guardian cell phone number:___________________________________________________ _ friends, or others for suggestions, but you may NOT look at their written work. If someone asks you for help, don’t show them your work. Instead, guide them hints and ask questions that will help them.

I have read this description and agree to do this assignment independently.

Name

Date

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

2

Perfect Squares Fill in as many values as you can FROM memory. You do NOT need to go in order. The goal is to assess your memory, so if you don’t know a fact immediately, write a “?” — do NOT calculate!

122 =

302 =

182 =

192 =

152 =

72 =

132 =

252 =

202 =

142 =

162 =

62 =

112 =

212 =

172 =

102 =

1002=

302 =

242 =

92 =

When you are done, list the facts below that you did not know by heart below. Try to learn them before school starts in September.

In Grade 8, you studied the Pythagorean theorem. Explain it below with a simple diagram. Explain how knowing perfect squares by heart can make Pythagorean Theorem problems easier for you?

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

Solving Linear Equations Answer the following examples of linear equations. You need to show your work. Remember your work must be your own. 1) What is the solution of the equation? Justify each step with words.

w 2 3

2) Find the solution of the equation. Justify each step with words.

6 x 8 7 7

3) What is the solution of the equation? Justify each step.

17 13 8x

4) A square field has an area of 479 ft 2 . What is the approximate length of a side of the field? Give your answer to the nearest foot. Justify your answer.

3

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

4

5) A mountain climber ascends a mountain to its peak. The peak is 12,740 ft above sea level. The climber then descends 200 ft to meet a fellow climber. Find the climber’s elevation above sea level after meeting the other climber.

6) A camera manufacturer spends $2250 each day for overhead expenses plus $6 per camera for labor and materials. The cameras sell for $16 each. a. How many cameras must the company sell in one day to equal its daily costs?

b. If the manufacturer can increase production by 50 cameras per day, what would their daily profit be?

7) Some people say that there are three Pythagorean Theorems:

a2 + b2 = c2 b2 = c2 – a2 a2 = c2 – b2 Use your skills solving equations to explain why the second and third equation actually come from the first equation.

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

Solving Proportions Solve the proportion below as many ways as you can think of. You need to show at least four different ways. You can ask people for inspiration (but your work must be your own!) 𝑥 10 = 8 40 Example methods include: Using factors of change across the fractions. Using factors of change within the fractions Cross multiplying. Making patterns. Multiplying both sides by the same value Simplifying fractions first Trial and Error

5

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

Basic Terms Term

Description in words

3 Examples from the real world

(If you don’t remember, look up in a dictionary!)

Point

Line

Line Segment

Plane

Write a sentence distinguishing what acute, obtuse, and right angles. Include diagrams with your sentence to illustrate what you have said.

6

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

Triangles Make a list of every type of triangle you have ever studied. The last row is fully blank so that you can add the type of triangle missing from the list. Type

Description in words (If you don’t remember, look up in a dictionary)

Scalene

isosceles

All angles are less than 90°

One angle is 90°

One angle is greater than 90°

Drawing of an example

7

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

8

Quadrilaterals The diagram below is a family tree showing the relationship of different kinds of quadrilaterals. Some names and descriptions have been filled in to get you started. Fill in the rest. Quadrilateral

Kite

(two sides parallel, other two sides congruent)

Square

A square has a LOT of properties. Write a paragraph about them below, using a labeled diagram and the correct vocabulary, including words such as sides, angles, 90°, parallel, diagonals

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

Transversals In the diagram below, lines m and n are parallel.

m

n

1 2 3 4

5 6 7 8

Make a long list of complete sentences describing everything you see in the diagram above. Use words such as parallel lines, transversal, vertical angles, alternate interior angles, corresponding angles, alternate exterior angles , and interior angles on the same side of the transversal Use numerical relationships, such as congruent (equal) and supplementary. 1) Example: The angles 1 and 4 are vertical angles. They are congruent (equal). 2)

When you are done, write “NO” next to any sentence that is FALSE if m and n are NOT parallel.

9

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

10

Sequences of Patterns For each example find the sequence of patterns. You need to show and justify your answer for each example. You should work on each example on your own. 1) Bobby has a set of tiles similar to the ones shown below. He says that his tiles have a total of 9 red triangles. Is 9 a reasonable number of triangles?

Fig. 1

Fig. 2

Fig. 3

2) The table shows the relationship between the number of white triangles and the total number of square tiles in each figure. Complete the table and extend the pattern. What is the total number of white triangles in afigure with 6 tiles?

Fig. 1

Fig. 2 Number of Square Tiles (s) 1 2 3 4 5

Fig. 3 Number of White Triangles (t) 4

2016-2017 Summer Math Preparation for Students Who Will Take Geometry

Proof In geometry class, you will learn to how to give proof that a mathematical statement is true. But the idea of proving something is true is not only part of mathematics — it’s part of life. Make a list of five situations in which someone must prove something. Situation In a real-life crime case

Who proved what?

How did they prove it?

In your own family life.

In a movie or TV show

In science

From your study of the bible

Look at the last column. What does proof always involve? Explain a couple of sentences.

11