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

It's an isosceles triangle

So if I had another 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.

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.

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.

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

One is bent to form a square, and the other is bent to form an equilateral triangle.

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

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.

And, if it's isosceles that means 2 of the sides are equal.

Geometric Isosceles Triangle

Equilateral Triangle

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

Now, this triangle right here is an isosceles triangle.

An isosceles trapezoid.

Because it's an isosceles trapezoid.

The perimeter of an equilateral triangle ABC is 3 times the perimeter of an equilateral triangle DEF.

Equilateral, D.

This is also an isosceles trapezoid.

Equilateral triangle with given two vertices

Base angles are equivalent on an isosceles triangle.

So this is an equilateral triangle.

I'm just going to assume I've constructed an equilateral triangle, so Triangle ABC is equilateral. and if it's equilateral, that means all of it's sides are equal, and lets say that it has an equilateral with sides of length x. so this is going to be x this is going to be x, and this is going to be x. we also know, based on what we seen from equilateral triangles before, that the measures of all of these angles are going to be 60 degrees.

We know that this is an equilateral triangle

This becomes an isosceles triangle again, very shaky.

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.

This whole base of the equilateral triangle is 2a.

So this is my best shot at an equilateral triangle.

Since this trapezoid is perfectly symmetric, since it's isoceles.

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

You could think of an isosceles triangle, over here.

And this comes to a general formula for the area of an equilateral triangle.

And then the other wire is going to form an equilateral triangle.

So now, you know all three sides are equal, so this is an equilateral triangle.

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

OK, so this is an equilateral triangle, all the sides are equal.

Well, if that angle is equal to this angle and we know it's isosceles, so if we know it's isosceles, that is equal to that, then that has to be equal to that, we know that all the angles are the same.

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

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

You obviosly can't have a right triangle that is equilateral, because an equilateral triangle has all, all of their angles have to be 60 degrees.

So I think what they say when they say an isosceles trapezoid, they are essentially saying that this side, it's a trapezoid, so that's going to be equal to that.

Since ancient times, the specific triangular degree of 51.51 isosceles, like that found in the energy grids of the Earth and the mysterious Great Pyramids of Egypt, have been known to conduct energy.

Now lets start with a triangle that we're very familiar with... so let me draw ourselves an equilateral triangle... so drawing the triangles is always the hard part.