Thread: the area of the triangles

1. the area of the triangles

Hello,
I have a small problem, so I decide to ask You for a help.

I don't know how improve that area AEF is equal to area of ABE and ADF triangels (together)

Have a nice day

2. Re: the area of the triangles

Originally Posted by rudzielica
Hello,
I have a small problem, so I decide to ask You for a help.

I don't know how improve that area AEF is equal to area of ABE and ADF triangels (together)

Have a nice day
you mean 'to prove' not 'improve'

Let $H$ be the point symmetric of $D$ with respect to $AF$

Area of triangle $AFH=$ area $AFD$

similarly construct a triangle $AEK$ whose area is equal to the area of triangle $AEB$

3. Re: the area of the triangles

Thank You for a help and correction.

However, I don't know where is point K?

And there isn't informationa that DF+BE=FE

4. Re: the area of the triangles

$K$ is symmetric of $B$ w.r.t. the line $AE$

$AFH$ and $AEK$ are right triangles

angle $AHF=90$ degrees
angle $AKE=90$ degrees

Show that area $AFH+AEK=AFE$

Note that $A,H,K$ are collinear