Geometric Isosceles Triangle

It's an isosceles triangle

Now, this triangle right here is an isosceles triangle.

Kind of like an isosceles triangle.

So if I had another isosceles triangle.

Base angles are equivalent on an isosceles triangle.

But we know that they're definitely isosceles triangle

This becomes an isosceles triangle again, very shaky.

An isosceles, let me write this, this is a right isosceles, i sos ce les triangle.

You could think of an isosceles triangle, over here.

Or another way to think about it is, if I have a right triangle that is also isosceles ,so a right triangle that is also isosceles.

And I can make the argument, but basically we know that RP, since this is an isosceles trapezoid, you could imagine kind of continuing a triangle and making an isosceles triangle here.

So the ratio of the sides and the hypotenuse, in a 45 45 90 triangle, or a right isosceles triangle.

So if you have a right isosceles triangle, whatever the two legs are, they're gonna have the same length, that's why it's isosceles.

I haven't seen the definition of an isosceles triangle anytime in the recent past.

This is an upside down isosceles triangle, this is a right side up one.

This is an isosceles triangle, so the two legs are going to be the same.

But you can have a right angle, you can have a right triangle that is isosceles.

They are going to be the same to each other, because this is an isosceles triangle.

so we're able to using constructing this triangle here we're able to both show its a similar and to construct this larger isosceles triangle to show

So a right isosceles triangle can also be called, and this is the more typical name for it

And the reason why that is interesting is it let's us know that this is an isosceles triangle

An altitude by definition is going to be perpendicular down here. Now, an isosceles triangle is perfectly symmetrical.

So even thought, it doesn't look that way based on the way, its drawn. This is actually an isosceles triangle.

Because these two base angles it's an isosceles triangle the two legs are the same so are two base angles

And isosceles triangle means that that side is equal to that side and that angle is equal to that angle.

So whatever isosceles triangle, if you have your 2 legs of it, the 2 base angles are going to be congruent

The sum of the square roots of two sides of an isosceles triangle is equal to the square root of the remaining side.

An isosceles trapezoid.

An isosceles trapezoid.

And the only way it's going to be an isosceles triangle is if this length is equal to that length, so let's just try it.

So two isosceles triangles.

Because it's an isosceles trapezoid.

This is also an isosceles trapezoid.

If you drop an altitude from the the top, or the unique angle, or the unique vertex in an isosceles triangle you will split it into two symmetric right triangles.

Any isosceles triangle, of that side equal to that side, if you drop an altitude, these two triangles are going to be symmetric, and you will have bisected the opposite side.

Two isosceles triangles with congruent vertex angles.

If that's one of my isosceles triangles.

Triangle AMO is a right triangle

Triangle FGI must be an obtuse triangle.

Triangle HlG, must be an acute triangle.

So an isosceles trapezoid means that the two sides that

Now, you have similar triangles that are isosceles or equilateral.

Triangle

triangle