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November 30, 2015
Posted by **p** on Saturday, January 2, 2010 at 3:51pm.

E(7,1) and F(4,6). Classify the triangle as:

a) isosceles or scalene

b) right angled or not

- geometry -
**MathMate**, Saturday, January 2, 2010 at 4:28pmAn 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.

- geometry-corr -
**MathMate**, Saturday, January 2, 2010 at 4:29pmL=√(8²+2²)=√68