geometry
posted by p .
The triangle DEF has vertices D(1,3)
E(7,1) and F(4,6). Classify the triangle as:
a) isosceles or scalene
b) right angled or not

geometry 
MathMate
An isosceles triangle has at least two equal sides.
To check this, we find the difference between the endpoints of each of the sides, and from that, we calculate the length using Pythagoras Theorem.
DE (1,3)(7,1)=(17,31)=(8,2)
L=√(8²+2*sup2;)=√68
EF (7,1)(4,6)=(74,16)=(3,5)
L=√(3²+(5)²)=√34
FD (4,6)(1,3)=(4(1),63)=(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 righttriangle. 
geometrycorr 
MathMate
L=√(8²+2²)=√68
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