Posted by p on Saturday, January 2, 2010 at 3:51pm.
An isosceles triangle has at least two equal sides.
To check this, we find the difference between the end-points of each of the sides, and from that, we calculate the length using Pythagoras Theorem.
D-E (-1,3)-(7,1)=(-1-7,3-1)=(-8,2)
L=√(8²+2*sup2;)=√68
E-F (7,1)-(4,6)=(7-4,1-6)=(3,-5)
L=√(3²+(-5)²)=√34
F-D (4,6)-(-1,3)=(4-(-1),6-3)=(5,3)
L=√(5²+3²)=√34
Since mEF=mFD, we conclude that the triangle DEF is isosceles.
Since mEF²+mFD²=mDE², we conclude that ∠EFD is a right angle, thus the triangle is a right-triangle.
L=√(8²+2²)=√68