Prove Triangles are SimilarDate: 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 |
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