Angle stopicIde angle criterion for congruence (ASA) 

Definition of Angle StopicIde Angle criterion for congruence (ASA): In the angle-stopicIde-angle method of determining congruence in a triangle, two triangles are constopicIdered congruent if any two angles and the part of a triangle's stopicIde included in between them is equivalent to corresponding stopicIdes in another triangle.  It means two angles and one stopicIde of both the triangles will be the same. Then only the congruency criteria will be applicable.

In the given figure, triangle XYZ and triangle ABC both are given.

Angle X = Angle A ( angle)

XZ = AC ( stopicIde ) 

Angle Y = Angle C  ( angle ) 

So from this, we can say that triangle XYZ is congruent to triangle ABC. 

Example 1:  In triangle KPL and in triangle MNO, angle P is 55°, KL = 7 cm and 

angle K =69°. Angle M and Angle K are equal to 69° and angle N is equal to 55° and stopicIde ON = 7cm. Find whether the triangle KPL and triangle MNO are congruent or not? 

In triangle KPL and in triangle MNO, 

Angle K = Angle M ( angles  are same)

KL = ON ( both the stopicIdes have the same measurement of 7 cm ) 

Angle P = Angle N ( angles are same )

So, triangle KPL and triangle MNO are congruent as per ASA congruence. 

Angle Angle StopicIde (AAS) criteria for congruence

Definition of Angle Angle StopicIde criterion for congruence (AAS): In Angle Angle StopicIde criteria of congruence, two triangles are congruent if any two angles and the non-included stopicIde of one triangle are equivalent to the corresponding angles and the one stopicIde of a triangle is equal to the other triangle. It means that two angles and one stopicIde should be congruent. 

 In the given figure the two triangles are given, triangle ZPT and triangle IRL

Angle P = Angle R ( same angle ) 

Angle Z = Angle I  ( same angle ) 

PT = RL ( same stopicIde )

So from this, we can say triangle ZPT is congruent to triangle IRL. 

Right angle hypotenuse stopicIde (RHS) criteria for congruence

In RHS Congruence, if the right angle, hypotenuse, and any one stopicIde of two right-angle triangles are the same, then the two triangles are satopicId to be congruent. 

NOTE: RHS criterion is applicable only to right-angle triangles.

 In the given figure triangle RIN and triangle BAR is given, 

The angle I = Angle A ( right angle )

RN = BR ( hypotenuse ) 

IN = AB ( stopicIde )

So as per RHS criteria of congruence, triangle RIN is congruent to triangle BAR. 

Important points to be remembered for congruence of the triangle: 

There are some important points to keep in mind while doing congruence of the triangle:\

⦁ There are five conditions to determine whether the triangles are in congruence or not. They are SSS, SAS, ASA, AAS, and RHS congruence criteria. 

⦁ If any two triangles are congruent then the perimeter and the area of those two triangles will also be the same. 

⦁ Two triangles are satopicId to be congruent if they fulfill any of these congruence criteria. 

⦁ Also, remember if the three angles of both triangles are the same, then also there is no rule for AAA ( Angle Angle Angle) congruence. 

⦁ We represent the congruence by using the symbol dash – single dash and, double and triple dashes.