Mathematics 8: Focus on Understanding
Diagrams for use in Chapter 3: Geometry I
The diagrams provided here have been created to act as companions to the various activities given in the Mathematics 8 textbook. They have been made from the information given in various explorations and questions for Chapter 3. Each diagram was originally created using The Geometer's Sketchpad and then copied into a Microsoft Word document. Files in both formats are listed below.
For your convenience, a .zip file has been created for each format. Downloading and expanding the .zip file will provide you with a folder containing all the documents listed for that format. Click HERE to go down the list to the links for the .zip files. A table of contents with links to the documents (opens in a web browser) is included in the word_files.zip file.
New for January 2009: We have added a new zip file, with all the Geometer's Sketchpad files included. These are the identical files, but translated into French. Click HERE to go to the zip file in French.
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Section of the Book
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Page
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Question
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Word file name
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Sketchpad file name
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| General Resources | ||||
| Coordinate Grid Paper | coordinate_grid.doc | coordinate_grid.gsp | ||
| Plain Grid Paper - 1 cm | grid_paper_1cm.doc | grid_paper_1cm.gsp | ||
| Plain Grid Paper - 0.5 cm | grid_paper_halfcm.doc | no file | ||
| Properties of Transformations | prop_trans_reflect_rot.doc | no file | ||
| Unit 3.1: Unique Triangles | ||||
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Discover the Math |
Page 110 |
8 (with construction) |
no file |
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Discover the Math |
Page 110 |
10 a) |
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Discover the Math |
Page 111 |
Example 1 a) |
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Discover the Math |
Page 111 |
Example 1 b) |
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Discover the Math |
Page 111 |
Example 2 a) |
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Discover the Math |
Page 111 |
Example 2 b) |
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Communicate the Key Ideas |
Page 112 |
2 a) |
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Communicate the Key Ideas |
Page 112 |
2 b) |
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Communicate the Key Ideas |
Page 112 |
2 c) |
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Check Your Understanding |
Page 112 |
3 |
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Check Your Understanding |
Page 112 |
5 all possibilities |
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Check Your Understanding |
Page 113 |
7 |
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Check Your Understanding |
Page 113 |
10 a) |
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Check Your Understanding |
Page 113 |
10 b) |
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Check Your Understanding |
Page 113 |
10 c) |
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Check Your Understanding |
Page 113 |
10 d) |
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Check Your Understanding |
Page 113 |
10 e) |
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| Unit 3.2: Prove Congruent | ||||
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Discover the Math |
Page 114 |
1 a) |
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Discover the Math |
Page 114 |
1 b) |
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Discover the Math |
Page 115 |
3 |
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Discover the Math |
Page 116 |
2 c) |
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Discover the Math |
Page 117 |
5 c) |
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Discover the Math |
Page 117 |
6 |
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Discover the Math |
Page 117 |
extra practice |
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Communicate the Key Ideas |
Page 118 |
Example 1 |
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Communicate the Key Ideas |
Page 118 |
Example 2 |
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Check Your Understanding |
Page 120 |
7 |
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| Unit 3.3: Transformations | ||||
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Discover the Math |
Page 121 |
1 a) |
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Discover the Math |
Page 122 |
1 d) |
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| Discover the Math | Page 122 | 4 | Page_122_4.doc | Page_122_4.gsp |
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Discover the Math |
Page 123 |
1 a) |
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Discover the Math |
Page 124 |
2 a) |
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| Discover the Math | Page 124 | 2 a) blank grid | Page_124_2a_blank.doc | Page_124_2a_blank.gsp |
| Discover the Math | Page 124 | 5 | Page_124_5.doc | Page_124_5.gsp |
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Discover the Math |
Page 125 |
1 a) |
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Discover the Math |
Page 125 |
1 b) |
no file |
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Discover the Math |
Page 125 |
1 j) |
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Discover the Math |
Page 125 |
2 a) |
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Discover the Math |
Page 126 |
3 a) |
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| Discover the Math | Page 126 | 4 | Page_126_4.doc | Page_126_4.gsp |
| Discover the Math | Page 126 | 5 Venn diagram | Page_126_5_Venn.doc | Page_126_5_Venn.gsp |
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Communicate the Key Ideas |
Page 127 |
Example 1 |
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Communicate the Key Ideas |
Page 128 |
Example 2 |
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Check Your Understanding |
Page 129 |
3 a) |
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Check Your Understanding |
Page 129 |
4 a) |
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Check Your Understanding |
Page 129 |
6 a) |
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Check Your Understanding |
Page 129 |
7 |
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Check Your Understanding |
Page 129 |
8 a) |
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Check Your Understanding |
Page 130 |
11 a) |
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Check Your Understanding |
Page 130 |
11 c) |
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Check Your Understanding |
Page 130 |
11 all hexagons |
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| Unit 3.4: Regular Polygons | ||||
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Discover the Math |
Page 133 |
4 e) table |
no file |
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Discover the Math |
Page 133 |
5 |
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Communicate the Key Ideas
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Page 135
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Example 2
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Check Your Understanding
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Page 135
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2 a)
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Check Your Understanding
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Page 136
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3 c) table
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no file
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Check Your Understanding
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Page 136
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8 a)
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Check Your Understanding
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Page 137
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9 a)
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Check Your Understanding
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Page 137
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9 c)
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Check Your Understanding
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Page 137
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9 e)
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Blank Polygons
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for Unit 3.4
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all on one page
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Blank Polygons
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for Unit 3.4
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Polygons (Central Angles)
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for Unit 3.4
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Zip file with all documents included
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Zip file with all Sketchpad documents in French
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Mathematics 8: Focus on Understanding
Diagrams for use in Chapter 9: Geometry II
The diagrams provided here have been created to act as companions to the various activities given in the Mathematics 8 textbook. They have been made from the information given in various explorations and questions for Chapter 9. Each diagram was originally created using The Geometer's Sketchpad and then copied into a Microsoft Word document. Files in both formats are listed below.
Please Note:
Files for Unit 9.3 are currently provided in two formats also. They are provided as .jpg images, suitable for printing.
Google Sketchup was used to create these 3D shapes, and files ending in .skp cannot be opened without that software installed. This is free software - click here to go to the download site. You will need to consult with your Board Technology Coordinator about having this software installed on computers in your school.
UNIT 9.3 files - Click Here to jump to the materials for this unit.
For your convenience, a .zip file has been created for each format. Downloading and expanding the .zip file will provide you with a folder containing all the documents listed for that format. Click HERE to go down the list to the links for the .zip files. A table of contents with links to the documents (opens in a web browser) is included in the word_files.zip file.
| Get Ready page 385 | Word file name | Microsoft PowerPoint | |
| Proportions within Relationships | - additional exercise | prop_within_rel.doc | |
| Proportional Reasoning Activity | proportional_reasoning.ppt | ||
| Get Ready page 387 | Word file name | Google Sketchup file name | Image file name |
| Platonic Solids | platonic_solids.doc | see files below | see files below |
| Tetrahedron | tetrahedron.skp | tetrahedron.jpg | |
| Hexahedron (cube) | hexahedron.skp | hexahedron.jpg | |
| Octahedron | octahedron.skp | octahedron.jpg | |
| Dodecahedron | dodecahedron.skp | dodecahedron.jpg | |
| Icosahedron | icosahedron.skp | icosahedron.jpg | |
| General Resources | Microsoft Word | Geometer's Sketchpad | |
| Coordinate Grid | coordinate_grid.doc | coordinate_grid.gsp | |
| Square Grid Paper - 1 cm | grid_paper_1cm.doc | grid_paper_1cm.gsp | |
| Square Grid Paper - 0.5 cm | grid_paper_halfcm.doc | ||
| Dot Paper - all | dot_paper.gsp | ||
| Dot Paper - Square 1 cm | dot_paper_1cm.doc | ||
| Dot Paper - Square 0.5 cm | dot_paper_halfcm.doc | ||
| Dot Paper - Isometric 1 cm | isometric_1cm.doc | isometric_1cm.gsp | |
| Mat Plan - blank | mat_plan_blank.doc | ||
| Pattern Blocks - all | Pattern_blocks.doc | Pattern_blocks.gsp | |
| Pattern Blocks - triangles | Pattern_triangles.doc | ||
| Properties of Transformations | prop_trans_reflect_rot.doc |
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Section of the Book
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Page
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Question
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Word file name
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Sketchpad file name
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| Unit 9.1: Dilatations | ||||
| Definition of Dilatations | Page_342_TR.doc | |||
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Discover the Math |
388 | 1 a, b, and c) | Page_388_1a_e.doc | Page_388_1a_b_c.gsp |
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Discover the Math |
388 | 1 d and e) | see above | Page_388_1d_e_f.gsp |
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Discover the Math |
389 | 2 a) table | Page_389_2a_table.doc | no file |
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Discover the Math |
390 | 2 c) and e) table | Page_390_2c_e_table.doc | no file |
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Discover the Math |
390 | 3 a and d) | Page_390_3a_d.doc | Page_390_3a_d.gsp |
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Discover the Math |
390 | 3 f) | Page_390_3f.doc | Page_390_3f.gsp |
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Discover the Math |
390 | 4 a) to j) | Page_390_4a_j.doc | Page_390_4a_j.gsp |
| Properties of Dilatations | Page_343_TR_dil_prop.doc | |||
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Communicate the Key Ideas |
391 | Example 1 | Page_391_Ex_1.doc | Page_391_Ex_1.gsp |
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Communicate the Key Ideas |
392 | Example 2 | Page_392_Ex_2.doc | Page_392_Ex_2.gsp |
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Check Your Understanding |
392 | 1 | Page_392_1.doc | Page_392_1.gsp |
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Check Your Understanding |
392 | 2 | Page_392_2.doc | Page_392_2.gsp |
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Check Your Understanding |
393 | 3 | Page_393_3.doc | Page_393_3.gsp |
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Check Your Understanding |
393 | 4 | Page_393_4.doc | Page_393_4.gsp |
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Check Your Understanding |
393 | 6 | Page_393_6.doc | Page_393_6.gsp |
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Check Your Understanding |
393 | 7 | Page_393_7.doc | Page_393_7.gsp |
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Check Your Understanding |
394 | 8 | Page_394_8.doc | Page_394_8.gsp |
| Check Your Understanding | 394 | 9 | Page_394_9.doc | Page_394_9.gsp |
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Check Your Understanding |
394 | 10 | Page_394_10.doc | Page_394_10.gsp |
| Unit 9.2: Similar Figures | ||||
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Discover the Math |
395 | 1 | Page_395_1.doc | Page_395_1.gsp |
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Discover the Math |
396 | 2 | Page_396_2.doc | Page_396_2.gsp |
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Discover the Math |
396 | 3 | Page_396_3.doc | Page_396_3.gsp |
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Discover the Math |
397 | 1 | Page_397_1.doc | Page_397_1.gsp |
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Discover the Math |
397 | 2 | Page_397_2.doc | Page_397_2.gsp |
| Discover the Math | 397 | 3 | Page_397_3.doc | Page_397_3.gsp |
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Communicate the Key Ideas |
399 | Example 1 | Page_399_Ex_1.doc | Page_399_Ex_1.gsp |
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Communicate the Key Ideas |
399 | Example 2 | Page_399_Ex_2.doc | Page_399_Ex_2.gsp |
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Check Your Understanding |
400 | 1 a) | Page_400_1a.doc | Page_400_1a.gsp |
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Check Your Understanding |
400 | 1 b) | Page_400_1b.doc | Page_400_1b.gsp |
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Check Your Understanding |
400 | 2 a) | Page_400_2a.doc | Page_400_2a.gsp |
| Check Your Understanding | 400 | 5 | Page_400_5.doc | Page_400_5.gsp |
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Check Your Understanding |
401 | 9 a) | Page_400_9a.doc | Page_400_9a.gsp |
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Check Your Understanding |
401 | 9 b) | Page_401_9b.doc | Page_401_9b.gsp |
| Check Your Understanding | 401 | 10 | Page_401_10.doc | Page_401_10.gsp |
| Check Your Understanding | 401 | 13 | Page_401_13.doc | Page_401_13.gsp |
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Check Your Understanding |
401 | 17 | Page_402_17.doc | Page_402_17.gsp |
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Unit 9.3: Cones & Cylinders |
Page | Question | Google Sketchup file | JPG image file |
| A: Cones & Pyramids | ||||
| Right Cone | right_cone.skp | right_cone.jpg | ||
| Oblique Cone | oblique_cone.skp | oblique_cone.jpg | ||
| Truncated Cone | truncated_cone.skp | truncated_cone.jpg | ||
| Right Square Pyramid | right_sq_pyramid.skp | right_sq_pyramid.jpg | ||
| Oblique Square Pyramid | oblique_sq_pyramid.skp | oblique_sq_pyramid.jpg | ||
| Right Pentagonal Pyramid | right_pent_pyramid.skp | right_pent_pyramid.jpg | ||
| Oblique Pentagonal Pyramid | oblique_pent_pyramid.skp | oblique_pent_pyramid.jpg | ||
| Right Equilateral Tri. Pyramid | right_eq_tri_pyr.skp | right_eq_tri_pyr.jpg | ||
| Right Triangular Pyramid | right_tri_pyramid.skp | right_tri_pyramid.jpg | ||
| Oblique Triangular Pyramid | oblique_tri_pyramid.skp | oblique_tri_pyramid.jpg | ||
| Right Hexagonal Pyramid | right_hex_pyramid.skp | right_hex_pyramid.jpg | ||
| Oblique Hexagonal Pyramid | oblique_hex_pyramid.skp | oblique_hex_pyramid.jpg | ||
| Right Heptagonal Pyramid | right_hep_pyramid.skp | right_hep_pyramid.jpg | ||
| Oblique Heptagonal Pyramid | oblique_hep_pyramid.skp | oblique_hep_pyramid.jpg | ||
| Right Octagonal Pyramid | right_oct_pyramid.skp | right_oct_pyramid.jpg | ||
| Oblique Octagonal Pyramid | oblique_oct_pyramid.skp | oblique_oct_pyramid.jpg | ||
| Right Nonagonal Pyramid | right_non_pyramid.skp | right_non_pyramid.jpg | ||
| Oblique Nonagonal Pyramid | oblique_non_pyramid.skp | oblique_non_pyramid.jpg | ||
| Right Decagonal Pyramid | right_dec_pyramid.skp | right_dec_pyramid.jpg | ||
| Oblique Decagonal Pyramid | oblique_dec_pyramid.skp | oblique_dec_pyramid.jpg | ||
| Discover the Math | 404 | 3 | P404_3a.jpg | |
| Discover the Math | 404 | 3 d) | ||
| Communicate the Key Ideas | 405 | 4 a) | Word file: Page_405_4a_table.doc | |
| Communicate the Key Ideas | 405 | 5 c) | P405_5c.skp | P405_5c.jpg |
| B: Cylinders & Prisms | Page | Question | Google Sketchup file | JPG image file |
| Right Cylinder | right_cylinder.skp | right_cylinder.jpg | ||
| Oblique Cylinder | oblique_cylinder.skp | oblique_cylinder.jpg | ||
| Truncated Cylinder | trun_cylinder.skp | trun_cylinder.jpg | ||
| Right Triangular Prism | right_tri_prism.skp | right_tri_prism.jpg | ||
| Oblique Triangular Prism | oblique_tri_prism.skp | oblique_tri_prism.jpg | ||
| Right Square Prism | right_sq_prism.skp | right_sq_prism.jpg | ||
| Oblique Square Prism | oblique_sq_prism.skp | oblique_sq_prism.jpg | ||
| Right Pentagonal Prism | right_pent_prism.skp | right_pent_prism.jpg | ||
| Oblique Pentagonal Prism | oblique_pent_prism.skp | oblique_pent_prism.jpg | ||
| Right Hexagonal Prism | right_hex_prism.skp | right_hex_prism.jpg | ||
| Oblique Hexagonal Prism | oblique_hex_prism.skp | oblique_hex_prism.jpg | ||
| Right Heptagonal Prism | right_hep_prism.skp | right_hep_prism.jpg | ||
| Oblique Heptagonal Prism | oblique_hep_prism.skp | oblique_hep_prism.jpg | ||
| Right Octagonal Prism | right_oct_prism.skp | right_oct_prism.jpg | ||
| Oblique Octagonal Prism | oblique_oct_prism.skp | oblique_oct_prism.jpg | ||
| Right Nonagonal Prism | right_non_prism.skp | right_non_prism.jpg | ||
| Oblique Nonagonal Prism | oblique_non_prism.skp | oblique_non_prism.jpg | ||
| Right Decagonal Prism | right_dec_prism.skp | right_dec_prism.jpg | ||
| Oblique Decagonal Prism | oblique_dec_prism.skp | oblique_dec_prism.jpg | ||
| Communicate the Key Ideas | 406 | 3 | P406_3.skp | P406_3.jpg |
| Communicate the Key Ideas | 406 | 4 (original cylinder) | P406_4_cylinder.skp | P406_4_cylinder.jpg |
| Communicate the Key Ideas | 406 | 4 (half - cylinders) | P406_4_horiz_split.skp | P406_4_horiz_split.jpg |
| Communicate the Key Ideas | 406 | 4 (half - non-cylinders) | P406_4_diag_split.skp | P406_4_diag_split.jpg |
| Communicate the Key Ideas | 406 | 4 (half - both options) | P406_4_cong_halves.skp | P406_4_cong_halves.jpg |
| Communicate the Key Ideas | 407 | Example 1 | P_407_Ex1.skp | |
| Communicate the Key Ideas | 407 | Ex 2 - solution 1 | P407_Ex2_iso_trap_prism.skp | P407_Ex2_iso_trap_prism.jpg |
| Communicate the Key Ideas | 407 | Ex 2 - solution 2 | P407_Ex2_kite_prism.skp | P407_Ex2_kite_prism.jpg |
| Check Your Understanding | 408 | 5 | P408_5.skp | P408_5.jpg |
| Check Your Understanding | 409 | 6 | Word file - Page_409_6a_table.doc | |
| Check Your Understanding | 409 | 7 - square | P409_7_square.skp | P409_7_square.jpg |
| Check Your Understanding | 409 | 7 - hexagonal | P409_7_hexagonal.skp | P409_7_hexagonal.jpg |
| Check Your Understanding | 409 | 11 a and b) | P409_11_a_b.skp | P409_11_a_b.jpg |
| Check Your Understanding | 409 | 11 e) | P409_11_e.skp | P409_11_e.jpg |
| Check Your Understanding | 409 | 11 f) - pentagons | P409_11_f_pentagons.skp | P409_11_f_pentagons.jpg |
| Check Your Understanding | 409 | 11 f) - hexagons | P409_11_f_hexagons.skp | P409_11_f_hexagons.jpg |
| Unit 9.4: Draw Polyhedra | Page | Question | Google Sketchup Diagram | |
| Discover the Math | 411 | 3 | P_411_3.skp | |
| Discover the Math | 413 | Example 2 | P_413_Ex_2.skp | |
| Check Your Understanding | 415 | 3 | P_415_3.skp | |
| Word (or pdf) file name | Sketchpad file name | |||
| Discover the Math | 411 | 3 c) | Page_411_3c.doc | Page_411_3c.gsp |
| Discover the Math | 412 | Perspective instructions | P_412_perspective_instruct.doc | |
| Discover the Math | 412 | Perspective wksheet | P_412_perspective_worksheet.doc | |
| Discover the Math | 412 | Perspective image | P_412_perspective_image.pdf | |
| Discover the Math | 412 | Example 1 | Page_412_Ex_1.doc | Page_412_Ex_1.gsp |
| Discover the Math | 413 | Example 2 | Page_413_Ex_2.doc | Page_413_Ex_2.gsp |
| Discover the Math | 414 | Example 2 f) | Page_414_Ex_2f.doc | Page_414_Ex_2f.gsp |
| Check Your Understanding | 415 | 2 | Page_415_2.doc | Page_415_2.gsp |
| Check Your Understanding | 415 | 3 | Page_415_3.doc | Page_415_3.gsp |
| Check Your Understanding | 415 | 3 solution | no file | Page_415_3_solution.gsp |
| Check Your Understanding | 416 | 9 | Page_416_9.doc | Page_416_9.gsp |
| Zip file with all documents included | geometry8ch9_all_files.zip |
