Similar TrianglesDate: 1/22/96 at 9:53:52 From: Timothy Hanna Subject: triangle ABC For triangle ABC whose vertices are A(6,3),B(1,5),C(-1,4), what are the vertices of a similar triangle whose perimeter is 5 times that of triangle ABC? Date: 5/30/96 at 15:49:11 From: Doctor Alain Subject: Re: triangle ABC We will build a triangle A'B'C' similar to ABC, but with a perimeter 5 times that of ABC. The triangle could be located anywhere, so we can put A' anywhere. Let's say A' = (6,3) = A. B' should be five times as far away from A' as B is from A. We don't need to know how far B is from A since B is 5 units to the left and 2 units higher than A, so we will put B' 25 units to the left and 10 units higher than A'. B' = (-19,13). We do the same for C', C' = (-29,8). Segment A'B' is over segment AB and 5 times longer. Segment A'C' is over segment AC and 5 times longer. So angle C'A'B' is equal to angle CAB. Two triangles with two sides proportionnal and the angle between the two sides equal are similar, and therefore the third side is also proportional, so B'C' is 5 times longer than BC. -Doctor Alain, The Math Forum |
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