Congruence of Triangle - class 7(2)

Congruence of Triangles:

Congruence is the term used to define an object and its mirror image. Two objects or shapes are said to be congruent if they superimpose on each other. Their shape and dimensions are same. In case of geometric figures, line segments with same length are congruent and angles with same measure are congruent. Let’s see criteria of congruence of triangles with proof.

CONGRUENCE OF TRIANGLES

A polygon made of three line segments forming three angles is known as Triangle.

Two triangles are said to be congruent if their sides have same length and angles have same measure. Thus two triangles can be superimposed side to side and angle to angle.

 Congruent triangles are triangles having corresponding sides and angles equal. Congruence is denoted by the symbol ≅.  They have same area and same perimeter.

Congruence of triangles can be predicted without actually measuring the sides and angles. Different rules of congruence of triangles are as follows:

1.      SSS (Side-Side-Side):

If all the three sides of one triangle are equivalent 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 angle included between the sides of one triangle are equivalent 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 side included between the angles of one triangle are equivalent 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 equivalent to the hypotenuse and a side of the second right- angled triangle, the right triangles are said to be congruent by RHS rule.