 So section 10.3 is made up of three theorems and then we're going to do a couple of example problems So this video goes over two of the arcs and chords theorems And then we'll do two more videos with two practice problems on each All right So what you need to do on your note sheet is first of all copy down this picture what you want to do is show a chord of AB another chord of CD and You should make them look like they're about congruent because the first arcs and chords theorem is what's written here? If two chords are congruent then their corresponding arcs are congruent Okay, so what we're looking at here when we draw this picture is that AB and CD are congruent chords and So that's where this part comes from right here if chord AB is congruent to chord CD Then what has to be true? Well from this theorem what has to be true is that arc? AB has to be congruent to arc CD So not only are the two chords congruent, but their arcs must be now this theorem works both ways So if I told you that the arcs were congruent you would be able to tell me that the chords are congruent So for this first theorem make sure you copy the picture Make sure you copy the theorem and then fill in that if the Segments or the chords AB and CD are congruent then their arcs are congruent Okay for arcs and chords theorem number two again I'm gonna need you to copy down a couple of things on your note sheet first of all I want you to draw this picture So look at what we have here. We have a diameter going from A to B right through the center of the circle And then we have a chord this chord which goes from V to T and Intersects the Diameter at Y so we have diameter AB Chord VT and the chord and the diameter intersect at this point Y Now what I want you to also do is copy down what theorem number two is it says that if a diameter is perpendicular to a chord So let's stop for a second and also put on our picture a 90-degree angle So if a diameter is perpendicular to a chord which we have here the diameter AB perpendicular to the chord VT then it bisects the chord and It's arc So what just happened is? this diameter bisected so cut in half VT and The arc VT so what's happened is we know that v y has to be congruent to T y and arc VB has to be congruent to arc TB So let's go ahead and write or fill in the rest of this statement if BA is remember this symbol is perpendicular right here perpendicular So if BA the diameter is perpendicular to TV the chord then two things are true Vy Which is a chord is? congruent to T y which is also a chord and VB Which is an arc is? congruent to Tb Which is an arc? Now remember the order of these letters don't matter so you could have written v y and y t or b v and b t but the these two theorems Make up what we're going to use for the first set of practice problems so the next video We're going to use these theorems to help us answer some questions