Proportions and Similar Triangles Lesson 8.6 Proportions and Similar Triangles

Lesson 8.6 Objectives Identify proportional components of similar triangles Use proportionality theorems to calculate segment lengths

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

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

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

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 =