Parallel Lines and Proportional
Parts
Triangle Proportionality Theorem
• If a line parallel to one side of a triangle intersects
the other two sides in different points, then it
divides those sides proportionally.
Converse of the Triangle Proportionality
Theorem
• If a line intersects two sides of a triangle in
different points and divides those sides
proportionally, then it is parallel to the third side.
In
and
B
Answer: 15.75
Find BY.
In
Determine whether
and AZ = 32.
Explain.
X
Answer: No; the segments are not in proportion since
Parallel Lines and Proportional
Parts
Midsegment of a triangle – A line segment
that connects the midpoints of two of its
sides.
Triangle Midsegment Theorem
• The segment that joins the midpoints of two
sides of a triangle is parallel to the third side
and its length is half the length of the third
side.
Triangle UXY has vertices U(–3, 1), X(3, 3), and Y(5, –7).
is a midsegment of
a. Find the coordinates of W and Z.
Answer: W(0, 2), Z(1, –3)
b. Verify that
Answer: Since the slope of
and the slope of
c. Verify that
Answer:
Therefore,
Parallel Lines and Proportional
Parts
Corollaries
6.1 – If three or more parallel lines intersect
two transversals, then they cut off the
transversals proportionally.
6.2 – If three or more parallel lines cut off
congruent segments on one transversal, then
they cut off congruent segments on every
transversal.
In the figure, Davis, Broad, and Main Streets are all
parallel. The figure shows the distances in city blocks
that the streets are apart. Find x.
Answer: 5
Find a and b.
Answer: a = 11; b = 1.5