Once the idea of congruence has been established, students need experience in recognising congruent shapes in embedded diagrams, and in drawing them in a variety of orientations.
Shapes which can be superimposed on each other are said to be congruent. They are the result of a rotation, translation or reflection or a combination of these transformations. Congruent shapes are used extensively in design.
- Explore real life patterns such as those in tiling and patchwork.
- Cut out shapes from within a design and place them on top of each other.
- Discuss the sequence of transformations required to map one shape onto another: translation, rotation and reflection.
- Use pattern blocks to construct designs based on congruence.
- Provide students with a cut-out of a specific shape which they can use to re-draw the shape in a new orientation.
For example, draw ABCD in the new orientation indicated by A’B’.
Subsequently, provide students with activities which require them to draw transformations of shapes without the aid of a real object.
Students find challenge in constructing designs which involve rotations.
- Provide objects which can be manipulated physically to assist.
- Use polar grid paper to complete the rotation and then trace the resulting shape onto square grid paper.
- Highlight the matching sides and angles in different colours to ensure that they are equal.
