 Hello friends welcome again to another session on circles and in the last few sessions we talked about lots of definitions different parts of circle different properties and Inside of the circle outside of the circle radius diameter chord segment secant and all that right now After learning all those definitions. We are going to talk about some theorems related to circles So in this case in this particular session We are going to discuss about this theorem and it says if two arcs of a circle or Of congruent circles are congruent then corresponding chords are equal. So first we will lay emphasis on Congruent right two arcs are congruent now for that we need to define something and that is two arcs are two arcs are congruent are Congruent congruent if if their Degree measure Measure are equal Okay, so what is meant by degree measures guys? So for example in this case if pq and rs both has to be of the same radius Let's say R R Okay, so pq is congruent to rs if this angle p oq is Equal to r o dash s right so hence they are congruent if Angle p oq is equal to angle r o dash s If that is the case radius is same then arc pq will be congruent to arc R s now these two arcs can be on the same circle as well. So let's say this is p dash q dash if p dash q dash also has same degree measure that is this angle Let's say this is theta. This is theta then we say p dash q dash and pq are congruent I hope you understood what congruent arcs are now so hence congruent arcs can be if you see within the same circle or With you know and in two circles, but these two these two circles must be congruent What are congruent circles two circles which can superpose each other? That means two circles which have same radii are called congruent circles. Okay. Now once that is clear Now, let's try to understand what this theorem is talking about it says that if pq pq is equal to rs Okay, if pq is equal to rs then The chord pq that is this side pq is equal to chord rs. That's what we have to prove Okay, let's try and prove. So if you see proof Will be something like this and very very simple in triangles O pq and triangle O dash r s we have O p is equal to o dash r y Radi I same radii. Isn't it radii are equal Radi are equal correct similarly O q is equal to o dash s y same logic radii are equal and angle p o q is equal to angle p sorry r o dash s right because same degree measure Same degree measure Okay understood hence it, you know it indicates something. What does it indicate indicates that? triangle O pq is congruent to triangle O dash Rs be very very careful with the order of vertices you have written why because otherwise congruence May not be established. Okay, so o is equal to o dash clearly angle p is equal to angle r and angle q is Equal to angle s so hence The order is correct. So and what is the criteria here? If you see this is side then angle then side So hence by s a s congruence Criteria right. This is what we learned in previous sessions as well. So s a s congruence criterion therefore We can say pq is equal to RS and you know this You will write this multiple number of times Cpc et which is Corresponding parts of sorry. Yeah corresponding parts of congruent triangles, right? So this is what we needed to establish, isn't it? So we have to establish that pq is equal to RS Okay, hence proved so two arcs If two arcs of a circle are congruent then corresponding chords are equal and hence proudi, right? hence Right Okay, so we'll take up another theorem in the next session. Hope you understood this theorem