SIMILAR TRIANGLES

Similarity

If two objects are similar, they would have the same shape and proportion.

Theorems to determine similarity.

If three angles of a triangle are equal to three angles of another triangle, then these triangles are similar and the sides opposite to equal angles are proportional.

If two angles of a triangle are equal to two angles of another triangle, then these triangles are similar.

If three sides of a triangle are proportional to three sides of another triangle, then these triangles are similar

If two sides of a triangle are proportional to two sides of another triangle and their including angles are equal then these triangles are similar.

Main points to remember. 

The line joining the midpoints of two sides of a triangle is parallel and half as long.

The centroid of a triangle divides the median into 2 : 1