00:01
We need to write the proof.
00:02
So we need to give the statements for this first proof.
00:06
So we're given that o is the midpoint of mp and nq.
00:10
So if it's a midpoint, that means it bisects mp.
00:15
So this would be congruent to this.
00:17
And then n -o is congruent to n -q.
00:21
So our first statement is our given statement, because that's what we're given.
00:25
And because it's the midpoint by definition of midpoint, that's why we're able to mark m -o is congruent as p -o and n -o is congruent as q -o.
00:42
And then we have vertical angles.
00:46
We have this angle and this angle are congruent to each other.
00:49
So angle m -o -n is congruent or equal to the measure of angle p -o -q, and that's because of vertical angles.
01:01
And so now we can say that the two triangles are congruent by side angle, side, congruence theorem so side angle side we need to prove that the following triangles are congruent so we're given that segment bd bd b b b b b b b b b b b b b b b b b b b b b b bx angle angle a bc and so that's given so then we can mark um abc this side is congruent to this side so then we can say that angle the measure of angle a, b, d is equal to the measure of angle c, b, d, definition of angle bisector.
02:08
Then we're given that segment bd is perpendicular to ac...