Equilateral Triangle

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

Equilateral, D.

It's an isosceles triangle

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

Equilateral triangle with given two vertices

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.

So if I had another isosceles triangle.

We know that this is an equilateral triangle

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

All the angles in a triangle have to add up to 180.

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

This whole base of the equilateral triangle is 2a.

So this is my best shot at an equilateral triangle.

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.

But if you have a 60, let me do it in another color, if you have a 60, 60, 60 triangle, all of the angles are 60 degrees, you're dealing with an equilateral 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.

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

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.

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

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

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

If you know two of the angles in a triangle, you know the third.

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.

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.

So I'm going to take this wire of length a and form an equilateral triangle out of it, right?

It is an equilateral triangle, at the base is a volcano between three castles, over which is a rainbow and the sun shining.

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

So you have Y Y which is 2Y 60 degrees, plus 60 degrees is going to be equal to 180 because the interior angles of any triangle,

Well it's an equilateral triangle so all the sides are the same, so this is 2a and this is 2a.

I want to figure out just given the information here so obviously I have a triangle here I have another triangle over here we were given some of the angles inside of these triangles.

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.

Equilateral

Select the triangle that has to be transformed onto a given triangle...

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.

So you can maybe view it as the sides are equal their weight is the same on either side.

Azimuthal Equidistant

So these are equivalent.

All of these statements are equivalent.

I love you both the same.