Chapter 8 – Geometry- Lesson 8-1 Relating Solids and Plane ...



Chapter 8 – Geometry- Lesson 8-1 Relating Solids and Plane Figures

Seatwork Content Text Pages 434 -437

Below is a study guide that you can use for this unit. Memorize the shapes and their names below. Practice each night so by the end of the unit these and other terms would be easy to remember.

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Chapter 8 – Geometry- Lesson 8-1 Relating Solids and Plane Figures

Seatwork Content Text Pages 434 -437

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Chapter 8 – Geometry- Lesson 8-1 Relating Solids and Plane Figures

Homework Content Text Pages 434 -437

Name: ________________________________________

Cube Triangular Rectangular Rectangular Prism Prism Pyramid

Remember that a solid figure has three dimensions.

Complete the chart below for each figure.

|Solid Figure |Number of faces |Number of Edges |Number of Vertices |

|Cube | | | |

|Triangular Prism | | | |

|Rectangular Prism | | | |

|Rectangular Pyramid | | | |

Label the following shapes

__________________ ___________________ ___________________

Chapter 8 – Geometry-

Lesson 8-2 Polygons Seatwork Content Text Pages 438 -439

Below is a study guide that you can use for this unit. Memorize the shapes and their names below. Practice each night so by the end of the unit these and other terms would be easy to remember.

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The following figure is not a polygon

as it is not a closed figure.

[pic]

A circle is not a polygon as it

does not have straight sides.

[pic]

Chapter 8 – Geometry-

Lesson 8-2 Polygons Seatwork Content Text Pages 438 -439

Remember a polygon is a closed plane figure made of line segments. A polygon is regular if all its sides are equal and all its angles are equal.

Directions: Name the polygon. Then tell how many sides it has.

[pic]

Chapter 8 – Geometry-

Lesson 8-2 Polygons Homework Content Text Pages 438 -439

Name: ________________________________________

Remember a polygon is a closed plane figure made of line segments. A polygon is regular if all its sides are equal and all its angles are equal.

Directions: Name the polygon. Then tell how many sides it has.

[pic]

Directions: Tell whether the shape is a regular polygon, irregular polygon or not a polygon.

[pic]

Chapter 8 – Geometry- Content Text Pages 440-441

Lesson 8-3 SEATWORK Lines, Line Segments, Rays, and Angles

Name: ________________________________________

Directions: Use the word bank to correctly label the picture.

[pic]

Directions: Use the word bank to correctly label the picture.

[pic]

Use the drawing on the right to answer the following questions

Name three line segments , _____, _____, ______

Name two rays _________, __________

Name an angle ___________________

Chapter 8 – Geometry-

Lesson 8-3 HOMEWORK Lines, Line Segments, Rays, and Angles

Content Text Pages 440-441

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GO RIGHT ON TO THE NEXT PAGE

Chapter 8 – Geometry-

Lesson 8-3 HOMEWORK Lines, Line Segments, Rays, and Angles

Content Text Pages 440-441

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GO RIGHT ON TO THE NEXT PAGE

Chapter 8 – Geometry-

Lesson 8-3 HOMEWORK Lines, Line Segments, Rays, and Angles

Content Text Pages 440-441

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Chapter 8 – Geometry- Lesson 8-4 Triangle & Quadrilaterals

Content Text Pages 444-447

Name: ________________________________________

Classify each triangle by its sides (isosceles, scalene, equilateral) AND then by its angles (acute, obtuse, right).

[pic]

Directions: Use the word bank to correctly label the picture.

[pic]

Chapter 8 – Geometry- Lesson 8-5 Circles

Content Text Pages 448-449

Name: ________________________________________

Use the word bank on the right to draw an arrow to each part of the circle.

[pic] For each circle shown, find the length of the diameter.

[pic]

Chapter 8 – Geometry- Lesson 8-6 Congruent Figures and Motions

Content Text Pages 452- 455

Name: ________________________________________

Slides, Flips, and Turns

 

Directions: Choose the correct answer to each of the following problems.

 

 

 

 

  

1. The above arrow moved 90° to the right. This is an example of a ______.

 

A. slide B. flip C. turn

 

 

 

2. The example below is a demonstration of a __________.

 

 

 

 

  A. slide B. flip C. turn

 

 

3. The change in the position of the triangles in Set A to the position of the triangles in Set B is an illustration of a __________.

 

 

 

 

 

 

 

  A. slide B. flip C. turn

 

 

  4. The example below is a demonstration of a __________.

 

 

 

 

   A. slide B. flip C. turn

 

 5. In the example below, the triangles going from left to right is an illustration of a __________.

 

 

 

 

 

  A. slide B. flip C. turn

 

  

6. What is it called when the arrow in picture A is moved up to the position in picture B?

 

 

 

 

 

 

  A. slide B. flip C. turn

 

  

7. The arrow below in picture B is a mirror image of the arrow in picture A. This transformation is called a __________.

 

 

 

 

 

 

A. slide B. flip C. turn

 

 

8. Moving the triangle from Point A to Point B is called a _________.

 

 

 

 

 

  

A. slide B. flip C. turn

 

 

 

 

9. The example below is a demonstration of a __________.

 

 

 

 

 

 

 

 

 

 

A. slide B. flip C. turn

 

 

 

10.

 

 

 

 

 

 

 

Which of the above illustrations represents a flip?

 

A. Figure A B. Figure B C. Figure C D. Figure D

Chapter 8 – Geometry- Lesson 8-7 Symmetry

Content Text Pages 456- 457

Name: ________________________________________

For each flag, draw the line of symmetry (if there is one).

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Chapter 8 – Geometry- Lesson 8-8 Similar Figures

Content Text Pages 458- 459

Name: ________________________________________

Do the figures in each pair appear to be similar? If so are they also congruent?

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Chapter 8 – Geometry- Lesson 8-10 Perimeter

Content Text Pages 464- 465

Name: ________________________________________

1. Mrs. Ames wants to buy carpet for the room shown below.

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2. Beth is making a lid for her jewelry box with square tiles, as shown below.

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3. Look at the rectangles below.

[pic]

Find the perimeter of the following polygons. The first three are REGULAR polygons.

[pic] [pic] [pic]

[pic] [pic]

Chapter 8 – Geometry- Lesson 8-11 Area

Content Text Pages 468- 471

Name: ________________________________________

Find the areas of the following shapes.

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Chapter 8 – Geometry- Lesson 8-13 Volume

Content Text Pages 468- 471

Name: ________________________________________

Find the volume of the following shapes.

V = _________ V = _________ V = _________

A rectangular Prism has a length of 7 cm,

a width of 4 cm, and a height of 3 cm.

What is the volume of this prism? ________________

The length of an edge of a cube is,

5 ft. What is the total volume of two

Cubes of the same size? ________________

If a cube has a volume of 64 cubic units,

How long is each edge? ________________

Find the volume of the following shape. The triangle is a right triagle.

________________

Chapter 8 – Geometry- Lesson 8-13 Circumference of Circles

Content

Name: ________________________________________

To find the circumference of a circle.

Firstly we need to find the radius

The radius is half the length of the diameter

r = [pic]

r = 3 cm

So C = 2 π r

C = 2 × 3.14 × 3

= 18.84 cm

Exercise 1

Find the circumference of each of the following circles

1. 2. 3.

4. 5. 6.

Chapter 8 – Geometry- Lesson 8-13 Circumference of Circles

Content

Name: ________________________________________

Find the CIRCUMFERENCEof the following circles

1. 2.

3. 4.

5. 6.

Chapter 8 – Geometry- Lesson 8-14 AREA of Circles

Content

Name: ________________________________________

Find the area of the following circles

1. 2.

3. 4.

5. 6.

Chapter 8 – Geometry- Lesson 8-13 Extra Circumference of Circles

Content

Name: ________________________________________

Exercise

1. A circular pond has a diameter of 3.2 m.

a) What is the area of the pond?

b) What is the circumference?

2. A baseball stadium has a circular patch with a radius of 100 metres.

a) The groundsman is going to use a fertilizer and needs to know the area of the pitch. What is the area?

b) He also needs to know what the distance is all the way round. What is this dimension called and what is its value?

3. The diameter of the Earth at the equator is rather difficult to measure – we would need to dig a very long tunnel!! It is much easier to measure the circumference. The circumference of the Earth is 40,000 km. Can you calculate its diameter?

You could use a calculator and trial and improvement but make a note of each trial and the result.

Chapter 8 – Geometry- Lesson Area

Content

Name: ________________________________________

For each of the following shapes find:

a) the perimeter or circumference

b) the area

1.

2.6 cm

4.3 cm

2.

5 cm

13 cm

3.

6 cm

5 cm 5 cm

10 cm

4.

Chapter 8 – Geometry- Lesson Area

Content

Name: ________________________________________

For each of the following shapes find:

a) the perimeter or circumference

b) the area

A window frame in the shape of a rectangle is 90 centimeters long and 40 centimeters wide What is the perimeter of the window frame?

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What is the area of the shaded part of the floor?

Find the Area of the following figures

[pic]

1.____________

2.____________

3. ____________

4.____________

5.____________

Tutorials

The area of a composite shape is calculated by splitting the shape into separate shapes. The area of each one is then calculated and the areas are added together to find the total area. In examples below the shapes have been divided into two shapes.

Example 1

Area of shape A = 6 × 4 = 24 cm2

B = 3 × 2 = 6 cm2

Total Area = 24 + 6

= 30 cm2

Example 2

Area of shape C = [pic] (5 × 4) = 10 cm2

D = 4 × 3 = 12 cm2

Total Area = 10 + 12

= 22 cm2

The distance around the edge of a circle has a special name. It is called the circumference.

The circumference is just like the perimeter but is only used when talking about circles.

If you know the radius or the diameter of a circle you can calculate its circumference.

The circumference is given by:

C = 2 π r

π is a special number and is always 3.14

Example 1

C = 2 π r

C = 2 × 3.14 × 5

Circumference = 31.4 cm

Example 2

Firstly we need to find the radius

The radius is half the length of the diameter

r = [pic]

r = 3 cm

So C = 2 π r

C = 2 × 3.14 × 3

= 18.84 cm

The area of a circle is given by

Area = π × (radius) 2

A = π r 2

Example

Area = π r 2

= π × 52

= 3.14 × 25

= 78.5 cm2

Remember that area always has square units. In this case since the radius is in cm, the area is in square centimetres (cm2)

In a parallelogram the opposite sides are parallel.

Parallelogram area = b × h

A = b × h

Base (b)

Example

6 cm

8 cm

Area = b × h

= 8 × 6

= 48

Area = 48 cm2

Height (h) Triangle Area = Base × Height = b × h

2 2

Base (b) A = b × h

2

Trapezium Area = (a + b) × Height (h)

Height 2

(h)

Base (b) A = (a + b) × h

2

-----------------------

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[pic]

[pic]

[pic]

[pic]

In a flat surfaced solid figure, each flat surface is called a face.

An edge is a line segment where 2 faces meet

A vertex is where 3 or more edges meet

[pic]

[pic]

[pic]

# of sides _______

# of sides _______

# of sides _______

# of sides _______

Word Bank

Triangle Quadrilateral Pentagon Hexagon Octagon

# of sides _______

1.4 cm

Word Bank

point line

line segment right angle

obtuse angle acute angle

straight angle ray

.

.

.

.

.

.

.

[pic]

[pic]

Word Bank

Intersecting lines

Parallel lines

Perpendicular lines

Word Bank

Rectangle square

Trapezoid rhombus

parallelogram

[pic]

Center

Chord

Radius

Diameter

15 ft

22 ft

103 ft

13 in

19 ft

22 in

|Set A |

|Set B |

|Picture A |

|Picture B |

|Picture A |

|Picture B |

|Point A |

|Point B |

|Figure A |

|Figure B |

|Figure C |

|Figure D |

What is the area of Beth’s jewelry-box lid?

How much carpeting does she need to buy to cover the floor area? 

The perimeter of rectangle Y is how many centimeters greater than the perimeter of rectangle Z?

P= __________

P= __________

P= __________

P= __________

P= __________

[pic]

12 cm

4 cm

8.2 cm

18 cm

3.4 cm

1.4 cm

8 cm

4 cm

2 cm

Area of a circle

5 cm

A

B

7 cm

4 cm

6 cm

4 cm

C

5 cm

D

3 cm

4 cm

Area of a triangle

2 cm

Area of a trapezium

(a)

[pic]

[pic]

8 cm

4 cm

Height

(h)

Circumference of a circle

A = _______

P = _______

5 cm

3.4 cm

6 cm

18 cm

A = _______

P = _______

A = _______

P = _______

A = _______

P = _______

A = _______

P = _______

[pic]

[pic]

4 ft

12 ft

3 ft

6 ft

4 ft

7 ft

8 ft

5 ft

5 ft

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h_$OJQJ)j†hŒ{$hŒ{$CJOJ[?]QJ[?]U[pic]^J[?]aJhŒ{$CJOJ[?]QJ[?]Draw segments to divide the following complex shape into rectangles. Find the areas of each rectangle and add.

Area = __________________

3ft

10 ft

11 ft

6 ft

Draw segments to divide the following complex shape into less complex shapes. Find the areas of each shape and add.

[pic] Area = __________________

12 ft

7 ft

9 ft

[pic]

[pic]

[pic]

7 in.

2 in.

5 in.

3 in.

9 in.

6 in.

4 in.

8 in.

4 in.

[pic]

4 ft

9 ft

3 ft

6 cm

5 cm

2 cm

8 cm

2.4 cm

12 cm

16.4 cm

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