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.

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. Signup and view all the answers

Match the following terms with their definitions:

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 Signup and view all the answers

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

shape (A) Signup and view all the answers

In similar polygons, corresponding angles are always equal.

True (A) Signup and view all the answers

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

scale factor Signup and view all the answers

Describe two ways to determine if two triangles are similar.

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). Signup and view all the answers

Match the following terms related to graphs with their definitions:

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. Signup and view all the answers

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

Weather patterns (A) Signup and view all the answers

A graph can only be drawn in one way.

False (B) Signup and view all the answers

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

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. 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.

scale Signup and view all the answers

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

Two sides are equal (B) Signup and view all the answers

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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Description

Test your understanding of geometrical figures, similarity principles, and related concepts like scale factors and properties of similar triangles. This quiz will cover identification of similar figures and their applications in real-world scenarios. Perfect for students learning about geometry and its practical uses.