Congruent Polygons
5 min
Narrative
The purpose of this activity is for students to connect rigid transformations with congruent figures. In this activity, students identify which figures are images of an original triangle under a translation. They may notice features of figures under a translation, such as parallel corresponding segments, or the orientation of the figure staying the same. This will be useful in upcoming activities as students describe a sequence of transformations from one figure to another.
Launch
Provide access to geometry toolkits. Allow for 2 minutes of quiet work time followed by a whole-class discussion.
Student Task
All of these triangles are congruent. Sometimes we can take one figure to another with a translation. Shade the triangles that are images of triangle ABC under a translation.
Sample Response
Synthesis
The purpose of this discussion is for students to articulate what features they can look for when they are identifying a translation. Ask students what they noticed about figures that were translations of triangle ABC.
If no students share these observations, suggest them now and ask students to discuss:
- The shape appears to be pointed in the same direction. A rotation may not have this property.
- The corresponding points go in the same order around the figure. A reflection does not have this property.
- Corresponding sides are parallel. This is a property of translating a line.
If time allows, choose a triangle that is not the image of triangle ABC under a translation, and ask students what rigid transformation would show that it is congruent to triangle ABC. If needed, demonstrate the rotation or reflection.
Anticipated Misconceptions
If any students assert that a triangle is a translation when it isn’t really, ask them to use tracing paper to demonstrate how to translate the original triangle to land on it. Inevitably, they need to rotate or flip the paper. Remind them that a translation consists only of sliding the tracing paper around without turning it or flipping it.
Standards
- 8.G.2·Understand that 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, describe a sequence that exhibits the congruence between them.
- 8.G.A.2·Understand that 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, describe a sequence that exhibits the congruence between them.