Parallel Lines and Proportional Parts

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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.

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Example 4-1c
Answer 15.75
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Example 4-2c
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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.

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Example 4-3h
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Example 4-3i
Answer W(0, 2), Z(1, 3)
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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.

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Example 4-4c
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
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Example 4-5d
Find a and b.
Answer a 11 b 1.5