Can someone help me map these two triangles?

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Answer 1 · 2018-02-12T09:18:43

#(AB) / (XY) = (BC) / (YZ) = (CA) / (FD) = 1/2#

Hence the two triangles are similar.

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In triangle ABC : coordinates of A(0,0), B(1,3), C(4,2)

In triangle XYZ : coordinates of X(-5,1), Y ( -3,-5), Z(3,-3)

Distance between two points is calculated using the formula

#d = sqrt((x2-x1)^2 + (y2-y1)^2)#

#vec(AB) = sqrt((1-0)^2 + (3-0)^2 = sqrt10#

#vec(BC) = sqrt((4-1)^2 + (2-3)^2) = sqrt10#

#vec(CA) = sqrt((4-0)^2 + (2-0)^2) = sqrt20#

#vec(DE) = sqrt((-5+3)^2 + (1+5)^2 = sqrt40 = 2sqrt10#

#vec(EF) = sqrt((3+3)^2 + (-3+5)^2) = sqrt40 = 2sqrt10#

#vec(FD) = sqrt((3+5)^2 + (-3-1)^2) = sqrt80 = 2sqrt20#

For two triangles are to be similar, their sides are to be in the same proportion.

i.e. #(AB) / (XY) = (BC) / (YZ) = (CA) / (FD)#

Let us check whether this condition is satisfied in the given sum.

#cancel(sqrt10)^color(red)1 / (2 cancelsqrt10) = cancel(sqrt10)^color(red)1 / (2 cancelsqrt10) = cancel(sqrt20)^color(red)1 / (2cancelsqrt20)#

#=>. 1/2 = 1/2 = 1/2#

Hence the two triangles are similar.