Savvas Learning Co Geometry Student Edition Chapter 1 Tools of Geometry Exercise 1.1 Nets and Drawings for Visualizing Geometry
Page 7 Exercise 1 Problem 1
Given:
To find an isometric drawing of the cube structure.
By using graph method.
The isometric drawing for the given figure should look like
The isometric drawing for the given figure should look like
Page 7 Exercise 2 Problem 2
Given:
To find the drawing is isometric, orthographic, a net, or none.
By using net method.
This shows a folded-out flat surface of a figure so it is a net drawing.
This shows a folded-out flat surface of a figure so it is a net drawing
Page 7 Exercise 2 Problem 3
Given:
To find the drawing is isometric, orthographic, a net, or none.
By using orthographic method.
This shows three separate views: a top view, a front view, and a right-side view so it is an orthographic drawing.
This shows three separate views: a top view, a front view, and a right-side view so it is an orthographic drawing.
Page 7 Exercise 2 Problem 4
Given:
To find the drawing is isometric, orthographic, a net, or none.
By using isomeric method.
This shows a three-dimensional figure using slanted lines to represent depth so it is an isometric drawing.
This shows a three-dimensional figure using slanted lines to represent depth so it is an isometric drawing.
Page 7 Exercise 2 Problem 5
Given:
To find the drawing is isometric, orthographic, a net, or none.
By using graph method.
None of the three drawings’ description fit the figure.
None of the three drawings’ description fit the figure.
Page 7 Exercise 3 Problem 6
Given: Isometric drawing and an orthographic drawing.
To find the differences and similarities between the given drawing.
By using isometric method.
In an isometric drawing, you see three sides of a figure from one corner view. In an orthographic drawing, you see three separate views of the figure.
In both drawings, you see the same three sides of the figure (top, front, and right).
Also both drawings represent a three-dimensional object in two-dimensions.
In an isometric drawing, you see three sides of a figure from one corner view. In an orthographic drawing, you see three separate views of the figure. In both drawings, you see the same three sides of the figure (top, front, and right). Also both drawings represent a three-dimensional object in two-dimensions.
Page 7 Exercise 4 Problem 7
Given:
To find the three-dimensional figure with its net.
By using hexagons method.
Looking at this shape, we see that it has bases of triangles and three sides that are rectangles. Therefore knowing this, the only one that fits is A.
Looking at this shape, we see that it has bases of triangles and three sides that are rectangles. Therefore knowing this, the only one that fits is A.
Similarly
Given:
To find the three-dimensional figure with its net.
By using hexagons method.
Looking at the shape we see that the base and all of the sides are triangles and thus the only net that fits is B)
Looking at the shape we see that the base and all of the sides are triangles and thus the only net that fits is B).
Page 7 Exercise 5 Problem 8
Given:
To find the net with its dimensions.
By using isometric method.
Start with the square that is shown on bottom.
First imagine the front side being lain down flat in front of the bottom.
Do the same with both sides and the back.
Then put the top square on any of the side that you have drawn. By looking at the book, label the sides appropriately.
Start with the square that is shown on bottom. first imagine the front side being lain down flat in front of the bottom. Do the same with both sides and the back. Then put the top square on any of the side that you have drawn. By looking at the book, label the sides appropriately.
Page 7 Exercise 6 Problem 9
Given:
To find the net with its dimensions.
By using isometric method.
A net is a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure.
The net for the figure should look like
The net for the figure should look like
Page 7 Exercise 7 Problem 10
Given:
To find the net with its dimensions.
By using isometric method.
Page 8 Exercise 8 Problem 11
Given:
To find an isometric drawing of each cube structure on isometric dot paper.
By using isometric method.
The isometric drawing for the given figure should look like:
The isometric drawing for the given figure should look like
Page 8 Exercise 9 Problem 12
Given:
To make an isometric drawing of each cube structure.
Using the method of isometric dot paper.
Let , An isometric drawing of each cube structure.
Isomeric dot paper is used to draw cube structure.
Page 8 Exercise 10 Problem 13
Given:
To make an isometric drawing of each cube structure.
Using the method of isometric dot paper.
Let, An isometric drawing of each cube structure
Isomeric dot paper is used to draw cube structure.
Page 8 Exercise 11 Problem 14
Given:
To make an isometric drawing of each cube structure.
Using the method of isometric dot paper.
Let, An isometric drawing of each cube structure
Isomeric dot paper is used to draw cube structure.
Page 8 Exercise 12 Problem 15
Given:
To make an orthographic drawing.
Using the method of isometric function.
Let, In an orthographic drawing, remember that:
An orthographic drawing shows the same three views of the isometric drawing (top, front, and right).Solid lines show visible edges.
Dashed lines show hidden edges.
The orthographic drawing for isometric drawing should look like:
An orthographic drawing for isometric drawing is drawned.
Page 8 Exercise 13 Problem 16
Given:
To make an orthographic drawing.
Using the method of isometric function.
In an orthographic drawing, remember that
An orthographic drawing shows the same three views of the isometric drawing (top, front, and right).
Solid lines show visible edges.
Dashed lines show hidden edges.
The orthographic drawing for isometric drawing should look like:
An orthographic drawing for isometric drawing is drawned.
Page 8 Exercise 14 Problem 17
Given:
To make an orthographic drawing.
Using the method of isometric function.
Let , In an orthographic drawing, remember that:
An orthographic drawing shows the same three views of the isometric drawing (top, front, and right).
Solid lines show visible edges.Dashed lines show hidden edges.
The orthographic drawing for isometric drawing should look like:
An orthographic drawing for isometric drawing is drawned.
Page 8 Exercise 15 Problem 18
Given:
To draw eight different nets for the solid given.
Using the method of multiple representation.
Let
1.
2.
3.
4.
5.
6.
7.
8.
The eight different nets for the solid is represented.
Page 8 Exercise 16 Problem 19
Given: 8 cubes
To make an isometric drawing of a structure.
Using the method of isometric function.
Let, A possible structure using 8 cubes is given:
The corresponding isometric drawing is given below
The isometric drawing is drawn.
Page 8 Exercise 16 Problem 20
Given: 8 cubes
To make an orthographic drawing of the structure.
Using the method of orthographic function.
Let
In an orthographic drawing, remember that:
An orthographic drawing shows the same three views of the isometric drawing (top, front, and right).
Solid lines show visible edges.Dashed lines show hidden edges.
The orthographic drawing for isometric drawing should look like:
The orthographic drawing is drawned.
Page 8 Exercise 17 Problem 21
Given: Draw a net of the can at the right.
To explain what shape are the top and bottom of the can and uncurl the body.
Using the method of rectangular function.
Let
The shape of the top and bottom of the can are circles.
If we uncurl the body of the can, the shape is a rectangle
which has a length equal to the circumference of each circle and a width equal to the height of the can.
So, a possible net should look like:
The shape at top and bottom of can is a circle. A possible net is described.
Page 8 Exercise 18 Problem 22
Given: German printmaker Albrecht Dürer first used the word net.
To find Why he choose the word net.
Using the method of three dimensional function.
Let, Maybe he used the word net because when you use a real net it can wrap around a solid object.
If it’s wrapped tightly the net can take on the overall shape of the wrapped object.
So similarly the printed pattern when you fold it up is like a net wrapping around an object.
The printed pattern when he folds it up is like a net wrapping, so he chooses the word net.
Page 8 Exercise 19 Problem 23
Given:
To match the package with its net.Using the method of cubic function.
Let
Visualize the right hand side and the left hand side each folding into a half of a cube.
These are the top and bottom.
The piece in the middle then holds them on top of each other.
The Above diagram matches correctly for the package.
Page 8 Exercise 20 Problem 24
Given:
To match the package with its net.
Using the method of cubic function.
Let
In the above case,looks like opening the triangular shape.
The above diagram matches correctly for the package.
Page 8 Exercise 21 Problem 25
Given:
To match the package with its net.
Using the method of cubic function.
Let
If you break down a Chinese takeout box it wouldn’t have mainly triangles but squares.
The Above diagram matches correctly for the package.
Page 9 Exercise 22 Problem 26
Given:
To make an orthographic drawing for the isometric drawing.
Using the method of isometric function.
Let
In an orthographic drawing, remember that:
An orthographic drawing shows the same three views of the isometric drawing (top, front, and right).
Solid lines show visible edges.
Dashed lines show hidden edges.
The orthographic drawing for isometric drawing should look like:
An orthographic drawing for isometric drawing is drawn.
Page 9 Exercise 23 Problem 27
Given:
To make an orthographic drawing for the isometric drawing.
Using the method of isometric function.
Let
In an orthographic drawing, remember that
An orthographic drawing shows the same three views of the isometric drawing (top, front, and right).Solid lines show visible edges.
Dashed lines show hidden edges.
The orthographic drawing for isometric drawing should look like:
An orthographic drawing for isometric drawing is drawn.
Page 9 Exercise 24 Problem 28
Given:
To make an orthographic drawing for the isometric drawing.
Using the method of isometric function.
In an orthographic drawing, remember that:
An orthographic drawing shows the same three views of the isometric drawing (top, front, and right).Solid lines show visible edges.
Dashed lines show hidden edges.
The orthographic drawing for isometric drawing should look like:
An orthographic drawing for isometric drawing is drawn.