Congruent Triangles

Congruent Triangles:




Congruent Triangles:

The concept of Congruent Triangles is explained in detail here. Every geometric figure has a shape and a size. Two circles of different radii have the same shape but their sizes are different. But if we draw two circles of the same radius both the shape and size will be the same. Such figures with the same shape and size are called congruent figures. We can check whether two figures are congruent or not by the method of superposition. We say that two triangles ABC and DEF are congruent if we can make one triangle fit exactly on the other.

In the above figure, the two triangles are congruent and we write . The sides which are equal in length are called the corresponding sides and the angles which are equal in measure are called the corresponding angles.

Conditions for Congruent Triangles:

When two triangles have (i) the same shape, and (ii) the same size, then they are said to be congruent triangles.

Symbol for congruency is
Draw with AB = 4 cm, AC = 5 cm, and .

Also with DE = 4 cm, DF = 5 cm and

Draw these triangles on a tracing paper. Now place fig(ii) on fig.(i), so that D is placed on A, DE along AB and F on the same side as C.
It is noticed that coincides with exactly fits on ABC.


We Can put the entire explanation of Congruent Triangles in a Nut shell.


SAS Axiom:

If two triangles have two sides of one equal to two sides of the other, each to each, and angles included by these sides are equal, then the triangles are congruent.
AAS Axiom:

If two triangles have two angles of one equal to two angles of the other, each to each and also one side of one equal to the corresponding side of the other, then the triangles are congruent.
SSS Axiom:

If two triangles have three sides of one equal to three sides of the other each to each, then the triangles are congruent.
RHS Axiom:

If two right triangles have their hypotenuses equal and one side of one equal to one side of the other, then the triangles are congruent.

Hope you like the above example of Congruent Triangles.Please leave your comments, if you have any doubts.