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CBSE Class 9 Maths Triangles

Congruence Criteria: SAS and ASA

Two Geometrical figures are congruent to each other, if they are of the same shape and size.
SAS congruence Axiom: Two triangles are congruent to each other, if any two sides and the included angle of one triangle are equal to the corresponding sides and included angle of the other triangle.
ASA Congruence Rule: Two triangles are congruent, if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle. The congruence of triangles also holds even if the side is not included between the angles i.e. AAS holds.

Properties of Isosceles Triangle

The name Isosceles is derived from the Greek word iso (same) and skelos (leg). Two sides of an isosceles triangle are equal in length.
Sides opposite to equal angles of a triangle are equal in length.
Angles opposite to equal sides of a triangle are equal in measure.

Congruence Criteria: SSS and RHS

If all three sides of one triangle are equal to the corresponding three sides of the other triangle, then the two triangles are congruent by S.S.S Congruence Rule.
If in two right triangles the hypotenuse and one side of one right triangle is equal to the hypotenuse and the corresponding side of the other right triangle, then the triangles are congruent by RHS Congruence Rule.

Inequalities in a Triangle

If two sides of a triangle are unequal, then the greater angle is opposite to the greater side.
If two angles of a triangle are unequal, the greater side is opposite to the greater angle
The sum of any two sides of a triangle is greater than the third side.
The difference between any two sides of a triangle is less than the third side.

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