Congruent Shapes

Understanding Congruent Shapes

  • Congruent shapes are identical in size, shape, and measure. These shapes look the same; however, they can be flipped, twisted, or turned.

  • Two shapes are said to be congruent if their corresponding sides and angles are equal. That means if we lay them on top of each other, they will coincide perfectly.

  • The symbol for congruence is ≅. If two triangles ABC and DEF are congruent, we would denote this as ABC ≅ DEF.

Identifying Congruent Shapes

  • When identifying congruent shapes, measure angles and lengths of sides. If all corresponding angles and side lengths are equal, the two shapes are congruent.

  • It’s not necessary for the shapes to face in the same direction to be congruent. One might be a reflected or rotated version of the other.

  • Even when reshaped (as long as it’s not stretched or shrunk), shapes can be congruent given that the side lengths and internal angles remain the same.

Congruent Triangles

  • Congruent triangles have the same size and the same interior angles, and their corresponding sides are of equal length.

  • There are four main rules or tests to determine if triangles are congruent: SSS (Side, Side, Side), SAS (Side, Angle, Side), ASA (Angle, Side, Angle) and RHS (Right angle, Hypotenuse, Side).

  • SSS (Side, Side, Side): All three corresponding sides are equal in length.

  • SAS (Side, Angle, Side): Two corresponding sides and the angle between them are equal.

  • ASA (Angle, Side, Angle): Two corresponding angles and the side between them are equal.

  • RHS (Right angle, Hypotenuse, Side): This rule works for right-angled triangles only. It states that if the hypotenuse and one other side are equal in the triangles, then the triangles are congruent.

Congruent Quadrilaterals

  • Like triangles, quadrilaterals can also be congruent. If two quadrilaterals have all four sides and all four angles equal, then they are congruent.

  • In Quadrilaterals, unlike triangles, knowing just one pair of corresponding sides or angles being equal is not enough to establish congruence.

Remember that congruence is a crucial concept in geometry. Practise identifying congruent shapes with various exercises and problems to be comfortable with this topic.