Geometrical Figures and Similarity Quiz

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Questions and Answers

The ratio between the corresponding sides of two similar triangles is called the ______.

scale factor

Which of the following is NOT a requirement for two triangles to be similar?

  • All corresponding sides are equal (correct)
  • Two corresponding sides are proportional
  • All corresponding angles are equal
  • Two corresponding angles are equal

A scale model of a building is always smaller than the actual building.

True (A)

Explain how scale factor can be used to find the missing length of a side in a similar triangle.

<p>If you know the scale factor and the length of one corresponding side in each triangle, you can multiply the known side length by the scale factor to find the missing length of the corresponding side in the other triangle.</p> Signup and view all the answers

Match the following terms with their definitions:

<p>Scale factor = The ratio between corresponding sides of similar figures Similar triangles = Triangles with equal angles but not necessarily equal sides Network diagram = A diagram showing connections between different entities Map = A graphical representation of a geographical area</p> Signup and view all the answers

Two polygons are considered similar if they have the same _____.

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

In similar polygons, corresponding angles are always equal.

<p>True (A)</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

Describe two ways to determine if two triangles are similar.

<p>Two triangles can be proven similar by showing that all corresponding angles are equal (AA Similarity), or by showing that all corresponding sides are proportional (SSS Similarity) or by showing that two sides are proportional and the included angle is congruent (SAS Similarity).</p> Signup and view all the answers

Match the following terms related to graphs with their definitions:

<p>Vertex = A point representing an object in a network. Edge = A line connecting two vertices, representing a connection between objects. Degree = The number of edges connected to a vertex.</p> Signup and view all the answers

Which of the following is NOT a real-world application of networks?

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

A graph can only be drawn in one way.

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

Explain how the concept of scale factors can be applied to enlarge or reduce a diagram.

<p>A scale factor is a ratio used to enlarge or reduce a diagram. Multiplying the side lengths of the original figure by the scale factor will produce a larger or smaller similar figure, preserving the shape but changing the size.</p> Signup and view all the answers

When working with scale drawings, the _____ is the ratio between the dimensions of the drawing and the actual object.

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

Which of the following is NOT a minimum condition for two triangles to be similar?

<p>Two sides are equal (B)</p> Signup and view all the answers

Flashcards

Similar Figures

Figures that have the same shape but may differ in size.

Corresponding Angles

Angles in two similar shapes that are equal.

Scale Factor

The ratio that relates the lengths of corresponding sides in similar figures.

Similarity Statement

A statement that expresses the similarity of two geometric figures, naming vertices in order.

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Triangle Similarity Tests

Methods to determine if two triangles are similar using specific conditions.

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Identifying Vertices

Naming the corners of a shape in a matching order.

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Area and Volume of Similar Shapes

The properties of areas and volumes that scale with the square and cube of the scale factor, respectively.

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Graph Elements

Parts of a graph including vertices (nodes) and edges (lines).

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Networks in Real World

Interconnected systems represented by graphs, such as social networks or supply chains.

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Proportional Relationships

The relationship between two quantities that are in a constant ratio.

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Similar Triangles

Triangles that have the same shape but not necessarily the same size, with equal corresponding angles and proportional sides.

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Corresponding Sides

Sides in different geometric figures that are in the same relative position.

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Shadow Exploration

Studying similar triangles through the lengths and angles of shadows cast by objects.

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Scale Models

Three-dimensional representations of objects that are scaled down or up in size while maintaining shape.

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Graphical Representations

Visual formats such as maps and floor plans that display spatial relationships.

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Map vs. Network Diagram

A map shows locations and distances; a network diagram shows connections and relationships.

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Area and Scale Factor

The change in area when a figure is scaled, calculated by squaring the scale factor.

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Surface Area and Volume Relationship

The way surface area and volume change when scaling a three-dimensional figure.

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Routine vs. Non-routine Problems

Routine problems have a standard method for solving; non-routine problems require creativity and varied approaches.

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Study Notes

Geometrical Figures and Similarity

  • Similar figures have the same shape but not the same size.
  • Corresponding angles in similar polygons are equal.
  • Corresponding sides of similar polygons are in the same proportion (ratio).
  • Vertices in similar figures are matched in the order of the similarity statement.
  • Scale factor is used to enlarge or reduce diagrams.
  • Scale factor relates corresponding side lengths in similar polygons and circles.
  • Scale factor can be used to find unknown sides in similar figures.
  • Scale drawings are used in practical applications, including maps and floor plans.

Similar Triangles

  • Minimum conditions for triangles to be similar must be identified.
  • Four tests exist to determine if two triangles are similar.
  • Properties of similar shapes and solids (e.g., areas and volumes ) can be established.
  • Relationships between scale factor, area, and volume of similar shapes are applicable in problem-solving.

Introduction to Networks

  • Graphs/networks represent systems of interconnected objects (nodes/vertices) by lines (edges).
  • Real-world applications of networks include social networks, supply chains, and communication infrastructure.
  • Elements of a graph include vertices, edges, and degrees.
  • Graphs can be drawn in multiple ways.

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