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This video is provided as supplementary material
for courses taught at Howard Community College and in this video I'm going to
talk about triangle congruence
and why side-side-angle congruence doesn't always work.
So let's get started. You know when you've got two triangles
and you want to show that they are congruent there are a number of different ways you can do
do this.
You might use side-side-side congruence or
side-angle-side or angle-side-angle or
angle-angle-side. What about side-side-angle?
Let's see if that's a possibility. What I've done
is drawn two angles that are congruent angles.
For each of the angles, one of the sides is a ray,
so it hasn't got a specific length. And for each of the angles
one of the sides is a line segment, so it's got a specific length,
and those line segments are congruent. And now I'm gonna try to form two triangles.
I'm going to do this with two sticks that are the same
length, so they would be congruent sides. Let's see what happens.
I could form a triangle here. And I could form the same triangle
at the other angle.
So I have two congruent triangles. The problem is this:
There's another kind of triangle I ca form. I can swing one of these sticks around
and form a triangle which is
very different from the other triangle. So what this means is
I've got a pair of congruent sides -- that was the sticks that I used.
I've got another pair of congruent sides --
those were the sides that I drew in. And I've got a pair of congruent
angles,
but I don't have a pair of congruent triangles.
So in this case side-side -angle
didn't work as a way to prove congruency.
Now notice that in this case I had an acute angle. Let's see what happens if I have
an obtuse angle.
So I've drawn
an obtuse angle. One side of the angle is a ray
and one side is a line segment. I'm going to take this stick and see how many
different triangles I can form.
And it looks like no matter how I move the stick
there's really only one place, one way that I can form
a triangle. So that means that
when my tangle is an obtuse angle,
when it's greater than 90 degrees,
then side-side-angle
will work. It will not work for an acute angle but
it will work for an obtuse angle. It will also work for a right angle.
Let's look at that. So I've got a right angle.
One side of the angle is
a ray, the other side is a line segment.
I can use a stick to form the third side
and there's only one way I can form that third side. So this will work also.
In other words, if I have a right angle it will work and if I have an obtuse angle it will it work.
It won't work with an acute angle. When I have a right angle,
instead of saying side-side-angle,
sometimes you'll see this referred to as just HL,
for hypotenuse-leg, because when you've got a right angle
the side opposite that angle is the hypotenuse
and the sides next to the angle are called to legs.
So if you've got hypotenuse-leg
as a kind of congruency with a right angle
then you know you've got two congruent triangles also.
So a right angle will work. We refer to that as HL.
Other than that you can use side-side-angle,
but be careful: you've got to have an obtuse angle.
If the angle is acute then
you can't p.rove the two triangles are congruent
Okay, take care, I'll see you next time.