00:01
This is a nice little proof with really only one or two steps to get to the end because they give us so much.
00:11
All right.
00:11
So our statements being the givens, we have h -o is parallel to e -n.
00:18
We have h -n intersect o -e at w.
00:28
And we have hw is, or the measure of hw is equal to the measure of nw.
00:41
And all of that is given.
00:44
All right.
00:45
Well, now our second thing is we need, right, so we have here one set of congruent sides.
00:53
We really either need another set of congruent sides or possibly even a set of congruent sides.
01:00
Angles and immediately i see congruent angles, an easy one i always looked for, is vertical angles.
01:09
Vertical angles are congruent.
01:16
Vertical angles are congruent.
01:17
So i can say that the two vertical angles i have here, angle h -w -o is congruent to angle n -w -e.
01:33
All right, because they are vertical angles, right? they share that middle section.
01:40
So if we have, this is roughly what we have, they're right here.
01:45
They share that center.
01:48
They're made by the same two intersecting lines.
01:52
Well, similarly now, we're going to have another set of congruent angles in angle h and angle n.
02:02
And those are going to be congruent because we're making use of the fact that we have these two lines.
02:08
And let me redraw this just so it looks a little better.
02:12
We have these alternate interior angles.
02:19
Okay...