Podcast
Questions and Answers
What is preserved when a geometric figure is subjected to rotations, reflections, and translations?
What is preserved when a geometric figure is subjected to rotations, reflections, and translations?
A two-dimensional figure can be similar to another if the second can be obtained from the first by a sequence of dilations only.
A two-dimensional figure can be similar to another if the second can be obtained from the first by a sequence of dilations only.
False
What is the criteria for triangle similarity?
What is the criteria for triangle similarity?
angle-angle criterion
When parallel lines are cut by a transversal, the angles created have a special property. They are _______________.
When parallel lines are cut by a transversal, the angles created have a special property. They are _______________.
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Match the transformations with their effects on two-dimensional figures:
Match the transformations with their effects on two-dimensional figures:
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What is the relationship between transformations and congruence?
What is the relationship between transformations and congruence?
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A sequence of rotations, reflections, and translations of a figure will always result in a congruent figure.
A sequence of rotations, reflections, and translations of a figure will always result in a congruent figure.
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What is the significance of angle measures in determining the similarity of two figures?
What is the significance of angle measures in determining the similarity of two figures?
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Dilations of a figure preserve its ______________
Dilations of a figure preserve its ______________
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Match the transformations with their effects on figures:
Match the transformations with their effects on figures:
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Study Notes
Properties of Transformations
- Rotations, reflections, and translations take lines to lines, and line segments to line segments of the same length.
- Angles are taken to angles of the same measure.
- Parallel lines are taken to parallel lines.
Congruence of Figures
- A two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations.
- Given two congruent figures, a sequence can be described to exhibit the congruence between them.
Effect of Transformations on Figures
- Dilations, translations, rotations, and reflections can be described using coordinates to show their effect on two-dimensional figures.
Similarity of Figures
- A two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations.
- Given two similar two-dimensional figures, a sequence can be described to exhibit the similarity between them.
Angle Properties
- Informal arguments can be used to establish facts about the angle sum and exterior angle of triangles.
- The angle-angle criterion for similarity of triangles can be demonstrated.
Critical Thinking and Problem Solving
- Rotations, reflections, and translations of a geometric figure preserve congruence, similar to how properties of operations preserve equivalence of arithmetic and algebraic expressions.
- A sequence of transformations can be explained to result in a congruent or similar triangle.
Mathematical Practices
- Physical models, transparencies, geometric software, or other tools can be used to explore the relationships between transformations and congruence and similarity.
- The structure of the coordinate system can be used to describe the locations of figures obtained with rotations, reflections, and translations.
- It can be reasoned that since any one rotation, reflection, or translation of a figure preserves congruence, then any sequence of those transformations must also preserve congruence.
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Description
Verify and demonstrate properties of geometric transformations, including congruent figures and preservation of lines, line segments, angles, and parallel lines.
