Questions and Answers
Which shows two triangles that are congruent by ASA?
Which shows two triangles that are congruent by AAS?
Which of these triangle pairs can be mapped to each other using a translation and a rotation about point A?
Which of these triangle pairs can be mapped to each other using a reflection and a translation?
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Which of these triangle pairs can be mapped to each other using two reflections?
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Are the triangles congruent? Why or why not?
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Two rigid transformations are used to map JKL to MNQ. The first is a translation of vertex L to vertex Q. What is the second transformation?
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Study Notes
Triangle Congruence: ASA and AAS
- ASA (Angle-Side-Angle) indicates triangles are congruent when two angles and the included side are equal.
- AAS (Angle-Angle-Side) indicates congruence when two angles and a non-included side are equal.
Triangle Mappings
- Translation and rotation can map congruent triangles when corresponding vertices align through these transformations.
- Reflection combined with translation can also map congruent triangle pairs, altering their orientation but maintaining size and shape.
- Two reflections can create a congruence transformation that preserves orientation and position.
Congruence Confirmation
- Triangles are confirmed congruent if they satisfy the conditions of ASA or AAS congruence criteria.
Rigid Transformations
- Rigid transformations include translations, rotations, and reflections, maintaining the congruency of shape and size.
- For example, mapping triangle JKL to MNQ involves a translation of vertex L to vertex Q, followed by a rotation about point L.
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Description
Test your understanding of triangle congruence concepts, specifically ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side) criteria. These flashcards will help reinforce your knowledge of congruency through the application of transformations such as translation, rotation, and reflection.
