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Proportions and Similar Triangles
Lesson 8.6 Proportions and Similar Triangles
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Lesson 8.6 Objectives Identify proportional components of similar triangles Use proportionality theorems to calculate segment lengths
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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
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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
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Theorem 8.6: Proportional Transversals
If three parallel lines intersect two transversals, then they divide the transversals proportionally. UW WY VX XZ =
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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 =
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