 Hello and welcome to the session in this session. We will discuss congruence of triangles two figures are congruent if they are of same shape and of same size Like if you consider these two circles, they are same radii. So they are the congruent figures or they are the congruent circles Now two triangles are congruent if these sides an angles of one triangle are Equal to the corresponding sides of the other triangle if you consider these two triangles ABC and PQR Such that the sides and angles of triangle ABC are equal to the corresponding sides and angles of the triangle PQR Then we say the triangle ABC is congruent to the triangle PQR under the correspondence A corresponds to P B corresponds to Q and C corresponds to R and this is the Symbolic form of writing the congruency of two triangles And it is very necessary to write the correspondence of vertices correctly for writing of congruence of triangles in symbolic form We have that in congruent triangles Corresponding parts are equal and we write it as CPCT. That is the corresponding parts of Congruent triangles Next we discuss criteria for congruence of triangles Our first criteria for congruence of triangles is SAS congruence rule According to which we have that two triangles are congruent if two sides and the included angle of one triangle are Equal to the two sides and the included angle of The other triangle as you can see for triangles ABC and PQR AB is equal to PQ BC is equal to QR and angle B is equal to angle Q so by SAS congruence rule We can say that triangle ABC is congruent to the triangle PQR Now the next congruence rule is ASA congruence rule which says that two triangles are congruent if Two angles and the included side of one triangle are equal To two angles and the included side of the other triangle For triangles ABC and PQR angle B is equal to angle Q angle C is equal to angle R Side BC is equal to the side QR so by ASA congruence rule We have triangle ABC is congruent to the triangle PQR Now the next congruence rule is AS congruence rule According to which we have the two triangles are congruent if any two pairs of Angles and one pair of corresponding sides are equal in Triangles ABC and PQR AB is equal to PQ angle B is equal to angle Q and the C is equal to angle R So by AS congruence rule we have triangle ABC is congruent to the triangle PQR Equality of three angles is not sufficient for congruence of triangles Therefore for congruence of triangles out of three equal parts one has to be a site next is SSS congruence rule which says that two triangles are congruent if three sides of One triangle are equal to the three sides of another triangle in Triangles ABC and PQR side AB is equal to PQ BC is equal to QR and AC is equal to PR so by SSS congruence rule we have triangle ABC is congruent to the triangle PQR Now the next congruence rule is the RHS congruence rule that is if in two right triangles the hypotenuse and one side of One triangle are equal to the hypotenuse and one side of the other triangle Then the two triangles are congruent like if you consider the two right triangles ABC and PQR The hypotenuse AC of triangle ABC is equal to the hypotenuse PR of the triangle PQR and one side BC of Triangle ABC is equal to the side QR of the triangle PQR Then by RHS congruence rule we say that triangle ABC is congruent to the triangle PQR and here we have RHS stands for right angle hypotenuse site Consider this figure in this we have triangle ABC and triangle PQR in which the side AB of triangle ABC is equal to the side PQ of the triangle PQR and side BC is equal to the side QR and this AD is the median of Triangle ABC and PM is median of Triangle PQR and it is given to us that this AD is equal to PM let's consider triangles ABD and PQM in This we have that AB is equal to PQ which is already given to us Then AD is equal to PM which is also given to us and BD would be equal to QM Since we have that BC is equal to QR So half of BC would be equal to half of QR That is we have BD is equal to QM So from here we get the triangle ABD is congruent to the triangle PQM by SSS criteria for congruence of triangles So since these two triangles are congruent so we can have that angle V is equal to angle Q by CPCT that is corresponding parts of congruent triangles Now we shall consider triangle ABC and Triangle PQR in this we have AB is equal to PQ already given to us Side BC is equal to side QR which is again given to us and angle B is equal to angle Q by a CPCT So we get triangle ABC is congruent to the triangle PQR by SAS criteria So this is how we can show the congruency of two triangles by using different criteria for congruence of triangles This completes the session hope you have understood the concept of congruence of triangles