Congruence of Triangles

Two lines segments are congruent if they have the same length

Two angles are gongruent if they have the same measure

Two circles are congruent if they have the same radius

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

When we write the congruence,it is very important to have the same order of corresponding parts

Congruence refers to the equal measures of all dimensions

Similarity refers to the similar appearance of figures where the measures need not be same.There can be a particular ratio between the two figures instead

How to find if the figures are similar or congruent?

Similarity can be found just by looking over it

Congruence can be proven when one figure is superimposed on the other

There are 4 main congruence criterions

SSS - Side Side Side

When each of the three sides of one triangle are equal to the corresponding three sides of another triangle,The triangles are congruent

SAS - Side Angle Side

When two sides and the included angle of one triangle is equal to the corresponding two sides and the included angle of another triangle, then the two triangles are congruent

ASA - Angle Side Angle

When two angles and the included side of one triangle is equal to the corresponding two angles and the included side of another triangle, then the two triangles are congruent

RHS - Right angle Hypotenuse Side

When the hypotenuse and side of one right-angled triangle is equal to the hypotenuse and side of another right-angled triangle, then the triangles are congruent