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Triangle inscribed in a Hexagon

Hey sorry if this is in the wrong place and if the picture is too small but I need some help

What can you say about a triangle that is inscribed in a hexagon, where the vertices of the triangle hits the midpoint of 3 sides of a hexagon?

if there is something about it please explain it to me so I can understand better, thanks.

Re: Triangle inscribed in a Hexagon

Re: Triangle inscribed in a Hexagon

sorry i just added it right now

Re: Triangle inscribed in a Hexagon

Is it a regular hexagon or an arbitrary hexagon?

Re: Triangle inscribed in a Hexagon

Re: Triangle inscribed in a Hexagon

ABCDEF is aregular hexagon. Name the three midpoints that form the triangle

Re: Triangle inscribed in a Hexagon

Hello, gfbrd!

Quote:

What can you say about a triangle that is inscribed in a regular hexagon,

where the vertices of the triangle are the midpoint of 3 sides of a hexagon?

What do they want me to say?

. . It has three sides.

. . It has three angles.

. . It is equilateral.

. . It has 60^{o} angles.

Okay, I'll get serious . . .

A regular hexagon is composed of six equilateral triangles of side *a.*

Consider the upper half of the hexagon.

Code:

` : - - a - - :`

* * * * *

* . . *

a * . . * a

*=================*

* . . *

* . . *

* * * * * * * * *

: - - a - - : - - a - - :

We have an isosceles trapezoid.

The side of the triangle is the *median*.

Its length is the *average* of the lengths

. . of the two parallel sides.

Hence, the side of the triangle is $\displaystyle \tfrac{3}{2}a.$

The triangle's perimeter is $\displaystyle \tfrac{3}{4}$ of the hexagon's perimeter.

The triangle's area is $\displaystyle \tfrac{3}{8}$ of the hexagon's area.

Re: Triangle inscribed in a Hexagon

There are two additional triangles which can be drawn meeting the general requirements

Re: Triangle inscribed in a Hexagon

Great thanks for your help everyone.

Re: Triangle inscribed in a Hexagon

Re: Triangle inscribed in a Hexagon