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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) criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
- AAS (Angle-Angle-Side) criterion indicates that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, the triangles are congruent.
Rigid Transformations
- Rigid transformations preserve the shape and size of figures in geometry.
- Common rigid transformations include translations, rotations, and reflections, which can often show congruence between triangles.
Mapping Triangles
- To map triangles using transformations:
- Translation and Rotation: If a triangle can be repositioned using a translation and a subsequent rotation about a point, it indicates congruence.
- Reflection and Translation: In some cases, triangles can be made congruent by reflecting one triangle over a line and then translating it to align with another triangle.
- Two Reflections: It is also possible to achieve congruence by performing two reflections.
Assessing Congruence
- To determine if two triangles are congruent:
- If they can be matched using either the ASA or AAS criteria, they are congruent.
- Basic checks can reveal congruence; for instance, comparing corresponding angles and sides.
Additional Transformation Example
- In the transformation of triangle JKL to triangle MNQ, the first transformation is a translation from vertex L to vertex Q. The second transformation required to complete the congruence is a rotation centered at vertex L.
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Description
Explore the criteria for triangle congruence through ASA and AAS, and understand the role of rigid transformations such as translations, rotations, and reflections. This quiz will test your knowledge on mapping triangles and the conditions that indicate their congruence.
