Congruent Shapes

Congruent Shapes

Understanding Congruency in Geometric Shapes

  • Define congruent shapes as shapes that are identical in form, having the same size and shape.

  • Understand that if two shapes are congruent, they can be transformed into one another through rotations, translations, and reflections only.

  • Comprehend that reflections, translations, and rotations are known as isometries as they do not change the size and shape of a figure.

  • Appreciate that all sides and angles of a congruent shape should match exactly when superimposed on the original shape.

Criteria for Congruency

  • Understand four main congruency rules: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Right Angle-Hypotenuse-Side (RHS).

  • Recall the Side-Side-Side (SSS) rule: If all three sides of one triangle are equal to the corresponding sides of another triangle, the triangle are congruent.

  • Understand the Side-Angle-Side (SAS) rule: If two sides and the included angle in one triangle are equal to corresponding two sides and included angle in another triangle, the triangles are congruent.

  • Comprehend the Angle-Side-Angle (ASA) rule: If two angles and the included side in one triangle are equal to the corresponding angles and side in another triangle, the triangles are congruent.

  • Recall the Right Angle-Hypotenuse-Side (RHS) rule: If in two right-angled triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, the triangles are congruent.

Applying Congruency Concepts

  • Recognize that congruent shapes have equal areas.

  • Understand that congruent shapes have equal perimeters.

  • Apply congruency rules to prove congruency in various geometric shapes and figures.

  • Use congruent shapes to solve geometric problems and real-life application problems.

  • Solve problems involving congruency in triangles and other polygons.

  • Acknowledge that non-identical shapes can still be congruent, and different orientations of a shape can be congruent to each other. Remember that being congruent doesn’t mean having the same orientation or being in the same position.