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### Prove Triangles are Similar

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Date: 12/16/95 at 20:9:28
From: Anonymous
Subject: similar triangles

How do you prove two triangles to be similar?
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Date: 3/11/96 at 21:23:23
From: Doctor Patrick
Subject: Re: similar triangles

Hi!  You can tell if two triangles are similar in a lot of different
ways, but all of them involve comparing sides and angles of the two
triangles.  If all of the sides of each triangle are similar to the
corresponding sides in the other triangle, or if all of the angles are
equal then the triangles are similar.  Also, since equal angles are
opposite similar length sides you can prove that two triangles are
similar when any of the following conditions are true:

1. If two sets of corresponding sides are similar and the angle
between them is equal. (SAS)

2. If two corresponding angles are equal and the side between them
is similar, (ASA)

3. If two angles are equal and another side is similar (AAS)

4. If, in a right triangle, the hypotenuse and one leg are both
similar (HL)

5. If all three sides are similar (SSS)

6. If all three angles are equal (AAA)

7. If two sides are similar and one angle is equal.

You should also know that any of these EXCEPT the last two can be used
to prove triangles equal if you change similar sides for equal ones.

Doctor Patrick, The Math Forum

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

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