Parallelogram that tells us that the opposites sides are parallel.

Equilateral Triangle

Parallelogram FGHl.

A rectangle, all the sides are parellel.

It's a parallelogram.

You decide to start a flexagon commitee together to explore the mysteries of flexagation.

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

So in order for all of the sides to be parallel, the opposite sides have to be the same length.

Got my parallelogram.

But that's a parallelogram.

This is not a parallelogram.

That's our parallelogram.

Equilateral, D.

It's not an equilateral triangle.

And that of course is a quadrilateral.

So the area of your parallelogram squared is equal to the determinant of the matrix whose column vectors construct that parallelogram.

You start with the original, simple, three faced hexaflexagon, which you call the trihexaflexagon.

Equilateral triangle with given two vertices

Parallelogram is shown below.

And made the beams going around the house.

Well, the equilateral triangle.

And since it's shaped like a hexagon and you flex it and flex rhymes with hex, hexaflexagon it is.

If we know the area of one of the parallelograms, we know the area of all of the parallelograms because they are congruent.

Really, if we could just prove that one of the sides are the same, then we know that all of the sides are the same.

If one pair of opposite sides of a quadrilateral is parallel, then the quadrilateral is a parallelogram.

And use it like a strip of paper to make a hexaflexagon.

And what's the height of this parallelogram going to be?

This is a rhombus, so all the sides are the same.

But anyway, back to the quadrilateral.

Male

So this is an equilateral triangle.

This is all done in between the ribs.

And we'd be dealing with an equilateral triangle.

It's a regular polygon, all the sides are the same.

Equilateral Hyperbola by Four Points

And so we don't know what these sides are.

The parallelogram generated by v2 and v1.

So that tells you that all the sides are the same.

So this is definitely a scalene triangle.

A quadrilateral, the sum of the angles are going to be 360 degrees.

The two triangles must be scalene.

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

Regular polygon, all the angles and all the sides are congruent.

For the quadrilateral shown below, a quadrilateral has four sides, measure of angle A plus the measure of angle C is equal to what?

So there's a couple of times when you know that a triangle is similar, is if the ratio of all the sides are equal.