Geometry Similar Polygons Quiz
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Questions and Answers

The three angles in a triangle sum to ___ degrees.

  • 360
  • 90
  • 180 (correct)
  • 120
  • 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.

    False (B)

    What is the meaning of the symbol '~' when used in a similarity statement?

    <p>The symbol '~' represents 'similar to'.</p> Signup and view all the answers

    The ratio of corresponding side lengths in similar polygons is called the ______.

    <p>scale factor</p> Signup and view all the answers

    Match the following terms with their definitions:

    <p>Corresponding angles = Angles that occupy the same relative position in two similar figures Corresponding sides = Sides that occupy the same relative position in two similar figures Scale factor = The ratio of corresponding side lengths in similar figures Similarity statement = An equation that states two figures are similar and names corresponding vertices in the same order</p> Signup and view all the answers

    If the scale factor between two similar triangles is 2, then the ratio of their corresponding sides is 1:2.

    <p>False (B)</p> Signup and view all the answers

    If two polygons are similar, the corresponding angles are:

    <p>Congruent (C)</p> Signup and view all the answers

    Two similar triangles have corresponding side lengths of 6 cm and 9 cm. What is the scale factor?

    <p>3/2 or 1.5</p> Signup and view all the answers

    Similar figures have the same ______ but different ______.

    <p>shape, size</p> Signup and view all the answers

    Match the following terms with their corresponding definitions:

    <p>Similar figures = Figures with the same shape but different sizes Scale factor = The ratio of corresponding side lengths in similar figures Corresponding sides = Sides in two similar figures that are in the same relative position Congruent angles = Angles that have the same measure</p> Signup and view all the answers

    If two triangles have two pairs of congruent angles, they are always similar.

    <p>True (A)</p> Signup and view all the answers

    Two triangles are similar if their corresponding angles are equal and their corresponding sides are in the same _____.

    <p>proportion (A)</p> Signup and view all the answers

    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?

    <p>2</p> Signup and view all the answers

    Simplify the following

    4:6

    <p>2:3</p> Signup and view all the answers

    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

    <p>1200 (D)</p> Signup and view all the answers

    Flashcards

    Scale Factor

    A ratio that compares the sizes of two similar figures.

    Similar Polygons

    Polygons that have the same shape but different sizes, with corresponding angles equal and sides proportional.

    Missing Sides

    Unknown lengths of sides in a similar figure, which can be found using the scale factor.

    Corresponding Sides

    Sides in two similar figures that are in the same relative position.

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    Using Scale Factor

    The process of applying the scale factor to find missing side lengths in similar figures.

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    Congruent Triangles

    Triangles that are identical in shape and size, with all sides and angles equal.

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    Minimum Conditions for Similarity

    Specific criteria needed to determine if two triangles are similar.

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    Angle-Angle Criterion

    If two angles of one triangle are equal to two angles of another, the triangles are similar.

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    Side-Angle-Side Criterion

    If two sides of one triangle are proportional to two sides of another, and the included angles are equal, the triangles are similar.

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    Triangle Similarity Tests

    Four tests used to determine if two triangles are similar, including AA, SAS, SSS, and HL.

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    Corresponding Angles

    Angles in the same position when comparing similar shapes, confirming their similarity.

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    Proportional Side Lengths

    The condition where corresponding side lengths of similar triangles maintain the same ratio.

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    Similarity Statement

    A notation to express that two polygons are similar, using the symbol (~) between the names of the figures.

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    Matching Vertices

    Identifying vertices of similar polygons in a specific order to establish congruent angles and proportional sides.

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    Identifying Corresponding Parts

    The process of recognizing which sides and angles match between two similar polygons.

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    Proportionality in Similarity

    The property that states that in similar polygons, the ratios of the corresponding side lengths are equal.

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    Similarity Conditions

    Conditions under which two polygons are declared similar; necessary are equal angles and proportional sides.

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    Utilizing Prior Knowledge

    Applying previously learned concepts, like corresponding sides, to new scenarios such as finding scale factors.

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    Similar Figures

    Figures that have the same shape but not necessarily the same size.

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    Minimum Conditions for Similar Triangles

    Criteria needed to determine if two triangles are similar.

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    Area in Similar Shapes

    The relationship of areas of similar shapes based on the square of the scale factor.

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    Graph

    A collection of nodes connected by edges representing relationships.

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    Vertex in a Graph

    A point where two or more edges meet.

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    Edge in a Graph

    A line connecting two vertices in a graph.

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    Degree in a Graph

    The number of edges connected to a vertex.

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    Practical Problems with Scale

    Real-world problems that involve using scale factors to find unknown lengths.

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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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    Description

    Test your understanding of the properties of similar polygons and triangles in this quiz. You will explore concepts such as corresponding angles, side lengths, and scale factors. Perfect for geometry students looking to reinforce their knowledge.

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