Congruence of triangles

Objective

To verify experimentally the different criteria for congruency of triangles.

Pre-requisite Knowledge

  • Basic knowledge of triangle types.
  • Basic knowledge of triangle properties.
  • Length and angle measurement skills.

Concept of congruence

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Rules for congruence of triangle

SSS(Side-Side-Side)

If all the three sides of one triangle are equal to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.

SAS(Side-Angle-Side)

If any two sides and the angle included between the sides of one triangle are equal to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.

ASA(Angle-Side-Angle)

If any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.

RHS(Right angle-Hypotenuse-Side)

If the hypotenuse and a side of a right- angled triangle is equal to the hypotenuse and a side of the second right- angled triangle, then the two right triangles are said to be congruent by RHS rule.