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### Similar Triangles

Date: 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

Associated Topics:
High School Coordinate Plane Geometry
High School Geometry
High School Triangles and Other Polygons
Middle School Geometry
Middle School Triangles and Other Polygons

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