What We Have Discussed

Figures which are identical i.e. having same shape and size are called congruent figures.

Three independentdependent elements to make a unique triangle.

Two triangles are congruent if the sides of one triangle are to the sides of another triangle and the corresponding angles in the two triangles are equal.

Also, there is a one-one correspondence between the vertices.

In Congruent triangles corresponding parts are equal and we write in short ‘CPCT’ for corresponding parts of congruent triangles.

SAS congruence rule: Two triangles are congruent if two sides and the angle of one triangle are equal to the corresponding two sides and the included angle of the other triangle.

ASA congruence rule: Two triangles are congruent if two angles and the included of one triangle are equal to two angles and the included side of other triangle.

Angles opposite to equal sides of an isosceles triangle are .

Conversely, sides opposite to equal angles of a triangle are .

SSS congruence rule: If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are .

RHS congruence rule: If in two right triangles the hypotenuse and one side of one triangle are equal to the and corresponding side of the other triangle, then the two triangles are .

If two sides of a triangle are unequal, the angle opposite to the longer side is .

In any triangle, the side opposite to the angle is longer.

The sum of any two sides of a triangle is than the third side.