MA19.GDA.25
Verify criteria for showing triangles are congruent using a sequence of rigid motions that map one triangle to another.
Verify criteria for showing triangles are congruent using a sequence of rigid motions that map one triangle to another.
Unpacked Content
UP:MA19.GDA.25
Vocabulary
- Corresponding sides and angles
- Rigid motions
- If and only if
- Triangle congruence
- Angle-Side-Angle (ASA)
- Side-Angle-Side (SAS)
- Side-Side->Side (SSS)
Knowledge
Students know:
- Characteristics of translations, rotations, and reflections including the definition of congruence.
- Techniques for producing images under transformations.
- Geometric terminology which describes the series of steps necessary to produce a rotation, reflection, or translation.
- Basic properties of rigid motions (that they preserve distance and angle).
- Methods for presenting logical reasoning using assumed understandings to justify subsequent results.
Skills
Students are able to:
- Use geometric descriptions of rigid motions to accurately perform these transformations on objects.
- Communicate the results of performing transformations on objects.
- Use logical reasoning to connect geometric ideas to justify other results.
- Perform rigid motions of geometric figures.
- Determine whether two plane figures are congruent by showing whether they coincide when superimposed by means of a sequence of rigid motions (translation, reflection, or rotation).
- Identify two triangles as congruent if the lengths of corresponding sides are equal (SSS criterion), if the lengths of two pairs of corresponding sides and the measures of the corresponding angles between them are equal (SAS criterion), or if two pairs of corresponding angles are congruent and the lengths of the corresponding sides between them are equal (ASA criterion).
- Apply the SSS, SAS, and ASA criteria to verify whether or not two triangles are congruent.
Understanding
Students understand that:
- If a series of translations, rotations, and reflections can be described that transforms one object exactly to a second object, the objects are congruent.
- It is beneficial to have minimal sets of requirements to justify geometric results (e.g., use ASA, SAS, or SSS instead of all sides and all angles for congruence).
