Question

What are the difference between Similar triangles and congruent triangles?

Answer 1

Differences between Similar triangles and Congruent triangles:

Similar triangles: Two triangles are said to be similar if they have same shape but may not of same size. Similarity is denoted by the symbol$~$.

Types of similarity

• SAS (Side - Angle - side) : Ratio of two corresponding sides are equal and their including angles are equal.
• SSS(Side - Side - Side ): If three corresponding sides are in the same ratio.
• AA (Angle - Angle ) : If two corresponding angles are equal.

Congruent triangles: Two triangles are said to be congruent if they have same shape and identical size. Congruence is denoted by the symbol$\cong$.

Types of congruency

• SAS (Side - Angle - side) : Two corresponding sides are equal and their including angles are equal.
• SSS(Side - Side - Side ): Three corresponding sides are equal
• ASA (Angle - Side - Angle ): Two angles are equal and their including sides are equal.
• AAS (Angle - Angle- Side ): Two angles are equal and one non included sides are equal.
• RHS (Right angle - Hypotenuse - Side ): If hypotenuse and a side of a right angled triangle and a hypotenuse and a side of a right angled triangle of second triangle are equal.

Thus, similar triangles have same shape but may not have same size and congruent triangles have same shape and same respective size