Podcast
Questions and Answers
The three angles in a triangle sum to ___ degrees.
The three angles in a triangle sum to ___ degrees.
- 360
- 90
- 180 (correct)
- 120
What is the relationship between corresponding angles in similar polygons?
What is the relationship between corresponding angles in similar polygons?
- They have the same measure. (correct)
- They are always equal. (correct)
- They are always supplementary.
- They are always congruent.
If two polygons are similar, their corresponding sides are always equal in length.
If two polygons are similar, their corresponding sides are always equal in length.
False (B)
What is the meaning of the symbol '~' when used in a similarity statement?
What is the meaning of the symbol '~' when used in a similarity statement?
The ratio of corresponding side lengths in similar polygons is called the ______.
The ratio of corresponding side lengths in similar polygons is called the ______.
Match the following terms with their definitions:
Match the following terms with their definitions:
If the scale factor between two similar triangles is 2, then the ratio of their corresponding sides is 1:2.
If the scale factor between two similar triangles is 2, then the ratio of their corresponding sides is 1:2.
If two polygons are similar, the corresponding angles are:
If two polygons are similar, the corresponding angles are:
Two similar triangles have corresponding side lengths of 6 cm and 9 cm. What is the scale factor?
Two similar triangles have corresponding side lengths of 6 cm and 9 cm. What is the scale factor?
Similar figures have the same ______ but different ______.
Similar figures have the same ______ but different ______.
Match the following terms with their corresponding definitions:
Match the following terms with their corresponding definitions:
If two triangles have two pairs of congruent angles, they are always similar.
If two triangles have two pairs of congruent angles, they are always similar.
Two triangles are similar if their corresponding angles are equal and their corresponding sides are in the same _____.
Two triangles are similar if their corresponding angles are equal and their corresponding sides are in the same _____.
What is the scale factor of two similar triangles if the corresponding sides of the larger triangle are twice as long as the corresponding sides of the smaller triangle?
What is the scale factor of two similar triangles if the corresponding sides of the larger triangle are twice as long as the corresponding sides of the smaller triangle?
Simplify the following
4:6
Simplify the following
4:6
George is reading a map with a scale 1:100. Find the actual distance (in centimetres) between two points that are 12cm apart on the map
George is reading a map with a scale 1:100. Find the actual distance (in centimetres) between two points that are 12cm apart on the map
Flashcards
Scale Factor
Scale Factor
A ratio that compares the sizes of two similar figures.
Similar Polygons
Similar Polygons
Polygons that have the same shape but different sizes, with corresponding angles equal and sides proportional.
Missing Sides
Missing Sides
Unknown lengths of sides in a similar figure, which can be found using the scale factor.
Corresponding Sides
Corresponding Sides
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Using Scale Factor
Using Scale Factor
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Congruent Triangles
Congruent Triangles
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Minimum Conditions for Similarity
Minimum Conditions for Similarity
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Angle-Angle Criterion
Angle-Angle Criterion
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Side-Angle-Side Criterion
Side-Angle-Side Criterion
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Triangle Similarity Tests
Triangle Similarity Tests
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Corresponding Angles
Corresponding Angles
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Proportional Side Lengths
Proportional Side Lengths
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Similarity Statement
Similarity Statement
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Matching Vertices
Matching Vertices
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Identifying Corresponding Parts
Identifying Corresponding Parts
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Proportionality in Similarity
Proportionality in Similarity
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Similarity Conditions
Similarity Conditions
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Utilizing Prior Knowledge
Utilizing Prior Knowledge
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Similar Figures
Similar Figures
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Minimum Conditions for Similar Triangles
Minimum Conditions for Similar Triangles
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Area in Similar Shapes
Area in Similar Shapes
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Graph
Graph
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Vertex in a Graph
Vertex in a Graph
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Edge in a Graph
Edge in a Graph
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Degree in a Graph
Degree in a Graph
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Practical Problems with Scale
Practical Problems with Scale
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Study Notes
Year 9 - Geometrical Representation
- Unit Duration: 5 weeks
- Unit Focus: 2-dimensional shapes, 3-dimensional objects, geometrical figures, properties of figures, networks, planar graphs, Eulerian trails, concepts of proportion, scale factors, similarity, and connections to real-life situations.
- Outcomes: Explore 2D and 3D objects, establish conditions for congruent/similar triangles, solve problems related to properties of similar figures, solve problems with graphs/networks properties
- Content: Identifying and describing similar figures, understanding properties of similar figures (corresponding angles are equal and corresponding side lengths are in proportion), using ratio and scale factors for similar figures and problems, developing and applying minimum conditions for similar triangles (4 tests), establishing and applying properties of similar shapes/solids, investigating areas and volumes of similar shapes/solids; and introduction to networks, real-world applications (social networks, supply chains, communication infrastructure), elements of a graph (vertex, edge, degree), different ways to draw a graph
- Assessment: In-class assessment (using congruent and similar triangles to solve mathematical problems involving plane shapes), summative assessment.
- Learning Activities:
- Exploring relationships between height and objects
- Defining similarity through scaled copies
- Exploring similar figures in art
- Exploring similarity statements (corresponding sides and angles)
- Applying scale factor in different contexts (diagrams, similar figures, triangles)
- Using scale in non-routine problems (e.g., Shadows, models in movies)
- Comparing scale drawings and other graphical representations (e.g., maps, floor plans)
- Understanding the relationship between scale factor, area, and volume of similar figures
- Exploring the similarities and differences between maps and network diagrams
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