If the measures of the corresponding sides of two triangles are
proportional then the triangles are similar. Likewise if the
measures of two sides in one triangle are proportional to the
corresponding sides in another triangle and the including angles
are congruent then the triangles are similar.
If a line is drawn in a triangle so that it is parallel to one
of the sides and it intersects the other two sides then the
segments are of proportional lengths:
Parts of two triangles can be proportional; if two triangles are
known to be similar then the perimeters are proportional to the
measures of corresponding sides.
Continuing, if two triangles are known to be similar then the
measures of the corresponding altitudes are proportional to the
corresponding sides.
Lastly, if two triangles are known to be similar then the
measures of the corresponding angle bisectors or the corresponding
medians are proportional to the measures of the corresponding
sides.
The bisector of an angle in a triangle separates the opposite
side into two segments that have the same ratio as the other two
sides:
Video lesson: Find the value of x in the
triangle