 Hello and welcome to the session. In this session we discussed the following question which says, in the given figure, a y perpendicular to z y and b y perpendicular to x y such that a y is equal to z y and b y is equal to x y prove that a v is equal to z x. First let's recall the SAS congruence rule according to this we have that if two sides and the included angle one triangle are equal to two sides and the included angle of the other triangle the two triangles are congruent. This is the key idea to be used in this question. Now let's proceed with the solution. This is the figure given to us in which we have a y is perpendicular to z y then b y is perpendicular to x y a y is equal to z y and b y is equal to x y and we need to prove that a v is equal to z x. Now since we have given that a y is perpendicular to z y so this means that angle a y z is equal to 90 degrees then b y is perpendicular to x y this means that angle b y x is equal to 90 degrees that is from here we have angle a y z is equal to angle b y x. Now adding angle a y x on both sides we get angle a y z plus angle a y x is equal to angle b y x plus angle a y x. Now from the figure you can see that angle a y z plus angle a y x is equal to angle x y z and this is for the equal to angle b y x plus angle a y x that is this angle angle b y a. So we have now got angle b y a is equal to angle x y z now in triangles a y b and z y x we have a y is equal to z y which is already given to us then b y is equal to x y this is also given to us and angle x y z is equal to angle b y a which we have already proved above. So this means triangle a y b is congruent to triangle z y x by s a s congruence rule. Now since both these triangles are congruent so we get a b is equal to z x since they are the corresponding parts of congruent triangle so they are equal and we were supposed to prove a b is equal to z x so hence proved this completes the session hope you have understood the solution for this question.