What Are Triangles ?

Chapter: 7

Congruent Figures

Two figures are said to be congruent, if they are of same shape and of same size.

Congruency Of Triangles

Two triangles are congruent, if sides and angles of one triangle are equal to the corresponding sides and angles of the other triangle.

Criteria Of Congruency Of Triangles

  • SAS (Side-Angles-Side) : If two sides and the angle between these two sides of one triangle are equal to two sides and the angle between these two sides of the other triangle, then the two triangles are congruent.
  • ASA (Angle-Side-Angle) : If two angles and the side between these two angles of one triangle are equal to two angles and the side between these two angles of other triangle, then the two triangles are congruent.
  • SSS (Side–Side–Side) : If three sides of one triangle are equal to the three sides of other triangle, then the two triangles are congruent.
  • RHS (Right angles – Hypotenuse–Side) : 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, then the two triangles are congruent.

Properties Of A Triangle

• Angles opposite to equal sides of a triangle are equal.

• The sides opposite to equal angles of a triangle are equal.

Some Important Facts

• Each triangle is congruent to itself.

• Difference between any two sides of a triangle is always less than its third side.

• Perimeter of a triangle is always greater than the sum of its three medians.

• Exterior angle of a triangle is always greater than the either of the opposite interior angles.

• Each angle of an equalateral triangle is 60°.