Similar Triangles Formula

Similar Triangles 1. Basic Proportionality Theorem (BPT) (also known as Thales Theorem)

In a triangle, a line drawn (DE) parallel to one side (BC) to interest the other side (AC) in distinct points (D and E) divides the two sides (AB and AC) in the same ratio.

AD AE = DB EC Corollary 1

Corollary 2

DB EC = AB AC AD AE = AB AC

2. (Converse of BPT). If a line divides any two sides of a triangle in the same ratio, the line must be parallel to the third side. 3. (AAA Similarity). If in two triangles, corresponding angles are equal, then the triangles are similar.

4. (SSS similarity). If the corresponding sides of two triangles are proportional, then they are similar. 5 (SAS similarity). If in two triangles, one pair of corresponding sides are proportional and the inclined angles are equal, then the two triangles are similar. 6. (Pythagorean Theorem). In a right triangle, the square of the hypotenuse is equal to the sum of the square of the other side.

AC 2 = AB 2 + BC 2 7. (Converse of Pythagorean theorem) In a triangle, if the square of one side is equal to the sum of the square of the other two sides then angle opposite to the first side is a right angle. That is a Triangle ABC is such that AB 2 + BC 2 = AC 2 , then Triangle ABC is a right triangle right angled at B. ________________________________________________