- [Instructor] So I have two triangles depicted here
and we have some information about each of those triangles.
We know that this side of this left triangle
has length eight.
We know that this side has length seven
and then we know that this angle is 50 degrees.
And on this triangle we see some things that look
a little bit familiar.
This triangle, this side has length eight.
This side has length seven.
And this angle right over here has a measure of 50 degrees.
So my question to you is,
can you definitively say, not assuming
that these are drawn to scale,
because they actually aren't, can you definitively say
that these triangles are congruent?
Or could you definitively say that they aren't congruent?
Or can you not say either?
Would you have to say that there's not enough information?
Pause this video and think about that.
So essentially what we have here are two pairs of sides
that have the same length and and angle,
but that angle is not between those two sides.
If the angle were here and here,
then we could use side, angle, side, side, angle, side
to deduce that, hey, these are congruent,
but that's not what we're dealing with.
We are dealing with side, side, angle.
Side, side, angle.
I'm saying the side and the side before the angle,
because if I don't do that it becomes a little bit crass.
So what we're really saying
is side, side, angle sufficient to prove congruency?
And the reason why it's not,
is that you can actually construct different triangles
with the same constraints.
For example, on this right most triangle
it could look like this,
or it could look like this.
The seven side could go down like this
and intersect just like that.
Now you might be saying, hey, that's not what it looks like.
It looks very similar, but remember,
we're not going on looks.
We have to go based on the information they've given us
and so you could just as easily, based on the information,
the constraints they've given us,
have a triangle like this.
And so the very fact that you can create
two different triangles that are clearly not congruent,
based on the exact same information,
the exact same constraints, tells you that
that information, those constraints,
are not enough to tell you
that these are congruent triangles.