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Geometry: Properties of Dilation and Similarity

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Geometry: Properties of Dilation and Similarity

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Questions and Answers

What is the definition of dilation in geometry?

Changing the shape of an object without altering its size.

Increasing the volume of an object without affecting its dimensions.

Reducing an object to a fraction of its original size while altering its shape.

Changing the size of an object without changing its shape. (correct)

Which property is true for corresponding angles in similar shapes?

Corresponding angles are complementary.

Corresponding angles can be acute or obtuse.

Corresponding angles are congruent. (correct)

Corresponding angles are always different.

If two triangles are similar and one side of the first triangle measures 6 cm while the corresponding side of the second triangle measures 9 cm, what is the scale factor?

2.5

1.5 (correct)

0.67

1.33

What happens to the second shape when the scale factor is less than 1?

<p>The second shape is smaller than the first. (C)</p> Signup and view all the answers

Which statement best describes the relationship of proportional sides in similar shapes?

<p>The ratio of corresponding sides is constant. (A)</p> Signup and view all the answers

Study Notes

Dilation

Dilation changes an object's size without altering its shape.
Size can increase or decrease, depending on the scale factor.

Properties of Similarity

Equal Angles

Similar shapes have congruent corresponding angles.
This helps identify similar shapes regardless of size differences.

Proportional Sides

Corresponding sides of similar shapes are proportional.
The ratio of corresponding side lengths remains constant.
For example, in similar triangles, the ratio of one side to its corresponding side remains the same for all corresponding sides.

Scale Factor

The ratio of corresponding sides in similar shapes is the scale factor.
The scale factor indicates how much one shape has been scaled (increased or decreased) to create the other.
Scale factor greater than 1 means the second shape is larger.
Scale factor less than 1 means the second shape is smaller.

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Description

Explore the properties of dilation and similarity in geometry. This quiz covers key concepts such as scale factors, equal angles, and proportional sides in similar shapes. Test your understanding and apply these principles to various geometric problems.