Prove Triangles are Similar

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

How do you prove two triangles to be similar?

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