Proportions

1
Lesson 8.6

• Proportions
• and
• Similar Triangles

2
Lesson 8.6 Objectives

• Identify proportional components of similar
  triangles
• Use proportionality theorems to calculate segment
  lengths

3
Triangle Proportionality

• Theorem 8.4Triangle Proportionality
• If a line parallel to one side of a triangle
  intersects the other two sides, then it divides
  the two sides proportionally.

• Theorem 8.5Converse of Triangle Proportionality
• If a line divides two sides proportionally, then
  it is parallel to the third side.

If RT/TQ RU/US, then TU // QS.
If TU // QS, then RT/TQ RU/US.
4
Using Theorems8.4 and 8.5

• Determine what they are asking for
• If they are asking to solve for x
• Make sure you know the sides are parallel!
• If they are asking if the sides are parallel
• Make sure you know the ratio of sides lengths are
  the same.

10/4 x/2
4x 20
x 5
5
Theorem 8.6Proportional Transversals

• If three parallel lines intersect two
  transversals, then they divide the transversals
  proportionally.

6
Theorem 8.7Proportional Angle Bisector

• If a ray bisects an angle of a triangle, then it
  divides the opposite side into segments whose
  lengths are proportional to the lengths of the
  other two sides.
• If CD bisects ?ACB, then