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Congruence and Isometry Quiz

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Questions and Answers

What is the formal definition of congruence in geometry?

Two figures have the same shape, size, and orientation.

Two figures have the same shape and size, or one is the mirror image of the other. (correct)

Two figures have the same shape, but not necessarily the same size.

Two figures have the same size, but not necessarily the same shape.

What transformations can make two sets of points congruent?

Translation, rotation, and reflection (correct)

Translation, reflection, and shearing

Scaling, rotation, and reflection

Translation, rotation, and dilation

In elementary geometry, when are two line segments congruent?

When they have the same midpoint

When they have the same slope

When they have the same length (correct)

When they have the same endpoints

What does it mean for two angles to be congruent?

They have the same measure Signup and view all the answers

When are two circles considered congruent?

When they have the same diameter Signup and view all the answers

What is the formal definition of congruence in geometry?

Two figures have the same shape and size, or one is the mirror image of the other Signup and view all the answers

Which transformations can be applied to make two figures congruent?

Translation, rotation, and reflection Signup and view all the answers

What is the difference between congruent and similar figures?

Congruent figures have the same shape and size, while similar figures have the same shape but not necessarily the same size Signup and view all the answers

When are two line segments considered congruent?

When they have the same length Signup and view all the answers

What is the condition for two circles to be congruent?

They have the same diameter Signup and view all the answers

Explain the formal definition of congruence in geometry and provide an example of two objects that are congruent.

Congruence in geometry means that two figures have the same shape and size. For example, two equilateral triangles are congruent if they have the same side length and the same angles. Signup and view all the answers

Describe the conditions under which two line segments are considered congruent in elementary geometry.

Two line segments in elementary geometry are considered congruent if they have the same length. Signup and view all the answers

What are the criteria for two angles to be considered congruent in geometry?

Two angles are considered congruent in geometry if they have the same measure. Signup and view all the answers

Explain the concept of congruence in relation to circles in geometry. Under what conditions are two circles considered congruent?

Two circles in geometry are considered congruent if they have the same diameter. Signup and view all the answers

Discuss the allowed operations that can make two distinct plane figures congruent on a piece of paper.

Two distinct plane figures on a piece of paper are considered congruent if they can be repositioned and reflected, but not resized, to coincide precisely with each other. Signup and view all the answers