 Hello and welcome to another problem solving session on congruent triangle guys. So the question says x and y are two points on equal sides ab and ac of triangle abc okay so ab and ac are equal and x and y are points on these sides such that ax so this side ax is we have to prove that xc is equal to yb xc is equal to yb okay so this is what we need so let me just clear this up yeah so let's begin understand how we can prove this question okay we have to prove that xc is equal to yb so as I told you in the previous sessions whatever is the final result let's go back from there assume that this is true assume that xc is equal to yb so that is true what else is given guys equals like ab is equal to ac is it that means this angle definitely is going to be equal to this angle right and if you see these two triangles x bc of which xc is the part and ycb of which yb is the part they are part of two triangles or these triangles right x bc and ycb these are the two triangles of which xc and yb are parts and of those two triangles one side bc is common okay and one angle is also equal if somehow I have proved that xb is equal to yc then by s s a and s criteria we will be able to prove the two triangles to be congruent and hence by will become equal to xc so this should be the line of action is it now how to prove so only element here is xb is equal to yc is that true yes it is true why because it's given that ab is equal to ac already c ab is equal to ac and ax and ay are given to be equal so clearly xb and hence yc will also be equal to hence I think we are done with the proof so let's write it formally so what is given so you have to write given what's given given is ab is equal to ab is equal to ac correct and ax is equal to ay x and y being the points on ab and ac respectively okay so we have to prove that xc xc so what are we going to write we are saying that since b is equal to ac given and ax is equal to ay this is also given therefore ab minus ax is equal to ac minus ay is it ac minus ay so what is ab minus ax if you see this is ab minus ax will give you this xb so and if you write xb and similarly here ac minus ay is this yc so xb is equal to s in so let's say in triangle observing or finding the two triangles of which the you know required result are parts or required signs xc and yb are parts is something we need to learn so in triangle xbc so pick this triangle up and triangle ycb so see the order in which I'm writing the points other vertices so we got what xb is equal to yc just prove above also angle abc or let's write xbc is equal to angle ycb ycb and what is the reason reason is angles opposite to equal sides equal sides in a triangle okay so this is done now let's come here and what do we get and third is bc is equal to the common side side so hence you can see side angle and side criteria so therefore we are writing I'm writing therefore by sas sas criteria triangle abc is congruent to not abc again so this is not abc guys this is this is this is xbc okay so triangle xbc is congruent triangle ycb so choice of or order of points again very very vital so therefore we can say xc so this is xc if we be equal to yb is equal to y corresponding parts of and hence we can say sas congruence criteria right I hope you understood this question and it's true