Triangles-Notes

•    SIMILAR TRIANGLES. Two triangles are said to be similar if

       (i)   their corresponding angles are equal and

       (ii)  their corresponding sides are proportional.

•    All congurent triangles are similar but the similar triangles need not be congruent.

•    Two polygons of the same numbers of sides are similar, if

       (i)   their corresponding angles are equal and

       (ii)  their corresponding sides are in the same ratio.

•    BASIC PROPORTIONALITY THEOREM. In a triangle, a line drawn parallel to one side, to intersect the other sides in distinct points, divides the two sides in the same ratio.

•    CONVERSE OF BASIC PROPORTIONALITY THEOREM. If a line divides any two sides of a triangle in the same ratio, the line must be parallel to the third side.