__Triangles__

**All congruent figures are similar, but it does not mean that all similar figures are congruent.**

**Two polygons of the same number of sides are similar, if:**

**Their corresponding angles are equal.**

**Their corresponding sides are in the same ratio.**

**Two triangles are similar, if:**

**Their corresponding angles are equal.**

**Their corresponding sides are in the same ratio.**

**If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.**

**If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.**

**If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar.**

**If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.**

**If in two triangles, sides of one triangle are proportional to the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.**

**If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.**

**The ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.**

**If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.**

**In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.**

**In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.**