### 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