Triangle Congruence and Transformations

Questions and Answers

Which shows two triangles that are congruent by ASA?

Option A

Option B (correct)

Option C

Option D

Which shows two triangles that are congruent by AAS?

Option B

Option C

Option A (correct)

Option D

Which of these triangle pairs can be mapped to each other using a translation and a rotation about point A?

Option A

Option C

Option D (correct)

Option B

Which of these triangle pairs can be mapped to each other using a reflection and a translation?

Option B Signup and view all the answers

Which of these triangle pairs can be mapped to each other using two reflections?

Option A Signup and view all the answers

Are the triangles congruent? Why or why not?

Yes, they are congruent by either ASA or AAS. Signup and view all the answers

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?

A rotation about point L. Signup and view all the answers

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.

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.