00:01
For this question, we're asked to prove that the perpendicular bisector of a chord of a circle is a diameter of the circle or contains the diameter of a circle, we could say.
00:10
All right.
00:11
So let's start with a chord.
00:14
So let's say start with cord d .e.
00:30
Right.
00:31
And let's construct perpendicular bisector.
00:44
All right.
00:44
So if we do that, that didn't go very well.
00:49
I'll try again.
00:51
That's a little closer.
00:53
Right and then um we can say we know every point all points on the perpendicular bisector are equidistant to e and d right so that's just a property of perpendicular bisectors any point on the perpendicular bisector if i draw a segment to d and a segment to e those two are going to be perpendicular right and that should be fairly easy to prove you can see here that this that we have two sides that are marked congruent in the triangles right now and of course they share the side so those two triangles these two triangles right here and that triangle and that triangle are congruent by side side side right and no matter where i draw the point to i'm always going to have well i guess i shouldn't assume that they're congruent but if i if i wanted to show that these are always congruent, i could say that, well, they have this side right here, and they have the right angles in common, so that the two triangles are congruent by side angle, side, and therefore corresponding sides of congruent triangle means that these are congruent.
02:50
That's how i should have said it the first time, right? and so no matter where i pick it, where i pick my point, right, as long as on this perpendicular bisector and i draw a segment to e and d and i get this triangle.
03:06
They share this side right here...