Online Course Discussion Forum

MCIC Geometry 3.10

 
 
Picture of Yuyu Wei
MCIC Geometry 3.10
by Yuyu Wei - Tuesday, 9 June 2020, 11:05 AM
 

Good morning! I am confused about 3.10.  Why have equation 1^2+(1-x)^2=2x^2?   Please help me, thank you.

 
Picture of Areteem Professor
Re: MCIC Geometry 3.10
by Areteem Professor - Wednesday, 10 June 2020, 1:54 PM
 

Using the Pythagorean Theorem in $\triangle ABE$ we have that $\overline{AB}^2 + \overline{BE}^2 = \overline{AE}^2$, so $1^2 + (1 - x)^2 = \overline{AE}^2$. Similarly, in $\triangle ECF$ we have $\overline{FC}^2 + \overline{CE}^2 = \overline{EF}^2$, so $x^2 + x^2 = \overline{EF}^2$. Since $\triangle AEF$ is an equilateral triangle, $\overline{AE} = \overline{EF}$, so $1^2 + (1-x)^2 = 2x^2$.

Picture of Yuyu Wei
Re: MCIC Geometry 3.10
by Yuyu Wei - Wednesday, 10 June 2020, 3:39 PM
 

Okay, I got it. Thank you.:) Have a good day.