Thread: square and angles problem

hey guys

A---------E----F----B
|..........................|
|..........................|
|..........................|
|..........................|
|..........................|
C-------------------D
ABCD is a aquare

Prove angle ACE is half angle FCD

thanks guys

Originally Posted by bloo.tomarto

hey guys

A---------E----F----B
|..........................|
|..........................|
|..........................|
|..........................|
|..........................|
C-------------------D
ABCD is a aquare

Prove angle ACE is half angle FCD

thanks guys

Presumably E is meant to be halfway between A and B; and F is halfway between E and B?

In that case, use some trigonometry to find the tan of each of those angles, and check that they are related by the formula As an extra hint, draw a vertical line from F down to the side CD, in order to create a right-angled triangle containing the angle FCD.