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Lesson 8.6

Lesson 8.6. Proportions and Similar Triangles. Lesson 8.6 Objectives. Identify proportional components of similar triangles Use proportionality theorems to calculate segment lengths. Theorem 8.4: Triangle Proportionality

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Lesson 8.6

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  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. 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. R T U Q S Triangle Proportionality If RT/TQ = RU/US, thenTU // QS. If TU // QS, then RT/TQ = RU/US.

  4. R 10 x T U Q S 2 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. UW VX = WY XZ Theorem 8.6:Proportional Transversals • If three parallel lines intersect two transversals, then they divide the transversals proportionally.

  6. AD CA = DB CB 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

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