Geometry Notes G.7 Using Proportionality Theorems
Mrs. Grieser
Name: ________________________________________ Date: __________________ Block: _______
We know: A triangle with a segment in its interior that is parallel to
one of the sides forms a similar triangle inside the original because
of AA.
Explain:________________________________________________________
Triangle Proportionality Theorem (and Converse)
A line is parallel to one side of a triangle IFF it intersects the
other two sides proportionally.
Example: Find RQ
Set up proportion:________________________________
Solve:____________________________________________
Theorem
If three parallel lines intersect two transversals, then they
divide the transversals proportionally.
Example: Find x.
Theorem
If a segment is an angle bisector, then it divides the opposite
side into segments whose lengths are proportional to the
lengths of the other two sides.
Example: Find x.
Geometry Notes G.7 Using Proportionality Theorems
Mrs. Grieser Page 2
Practice:
a) Determine whether
PQ || LM .
b) Find ST.
c) Find DE.
d) Find AD.
e) Determine whether MO || LP
f)
g) A brace is added to a tree house as shown.
Explain why the brace is not parallel to the
floor.
h) On the map below, Idaho Avenue bisects the
angle between University Avenue and Walter
Street. To the nearest yard, what is the
distance along University Avenue from 12th
Street to Washington Street?
A farmer’s land is divided by a newly
constructed interstate. The distances shown
are in meters. Find the distance CA between
the north border and the south border of the
farmer’s land.