geometry

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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 -

    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.

  • geometry-corr -

    L=√(8²+2²)=√68

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