Honors Geometry Section 8.5
Indirect Measurement &
Additional Similarity Theorems
Similar triangles can be used to
find the height of objects.
Proportional Altitudes Theorem
If two triangles are similar, then
corresponding altitudes are
proportional to a pair of
corresponding sides.
Let’s think about why this theorem is true.
Assume ABC ~ WXY , why is
AD AC

WZ WY ?
Proportional Medians Theorem
If two triangles are similar, then
corresponding medians are
proportional to a pair of
corresponding sides.
Proportional Angle Bisectors Theorem
If two triangles are similar, then
corresponding angle bisectors are
proportional to a pair of
corresponding sides.
The triangles shown are similar. Solve for x.
The triangles shown are similar. Solve for x.
Proportional Segments Theorem
An angle bisector of a triangle
divides the opposite side into
segments which are proportional
to the remaining two sides.
Solve for y.