1. Proportions and Similar Triangles
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 8.4: Triangle Proportionality
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
Theorem 8.5: Converse of Triangle Proportionality
If a line divides two sides proportionally, then it is parallel to the third side. Q S R
If RT/TQ = RU/US, then TU // QS.
If TU // QS, then RT/TQ = RU/US. T U

4. Using Theorems 8.4 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. Q S R
10/4 = x/2 x 10 2 4
4x = 20 T U
x = 5

5. Theorem 8.6: Proportional Transversals
If three parallel lines intersect two transversals, then they divide the transversals proportionally. UW WY VX XZ =

6. Theorem 8.7 Proportional 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 AD DB CA CB =