Rectangle ABCD has coordinates A(0,0), B(o, 10), C(6, 10), and D(6, 0). E is the midpoint of AB, and F is the midpoint of CD. How do you prove that EF = BC?

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Answer 1 · 2017-12-14T17:58:23

A Proof is give in the Explanation Section.

#E# is the midpoint of #AB,#

where, #A=A(0,0), and, B=B(0,10).#

#:. E=E{((0+0)/2),((0+10)/2)}=E(0,5).#

Similarly, #F=F(6,5).#

Now, #E(0,5), F(6,5) rArr EF^2=(0-6)^2+(5-5)^2, i.e.,#

#EF=6...........................................................................<<1>>.#

#B(0,10), C(6,10) rArr BC^2=(6-0)^2+(10-10)^2.#

#:. BC=6...................................................................<<2>>.#

From #<<1>> and <<2>>, EF=BC.#

Q.E.D.