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8.6: Proportions and Similar Triangles
GEOMETRY: Chapter 8 8.6: Proportions and Similar Triangles
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Theorem 8.4. Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two side proportionally. Image taken from: Geometry. McDougal Littell: Boston, P. 397.
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Theorem 8.5. Converse of the Triangle Proportionality Theorem
If a line divides two sides of a triangle proportionally, then it is parallel to the third side. Image taken from: Geometry. McDougal Littell: Boston, P. 397.
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Ex. 1: Image taken from: Geometry. McDougal Littell: Boston, P. 398.
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Ex. 1: Answer: 9 Image taken from: Geometry. McDougal Littell: Boston, P. 398.
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Ex. 2: A brace is added to a tree house as shown. Explain why the brace is not parallel to the floor. Image taken from: Geometry. McDougal Littell: Boston, P. 389.
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Ex. 2: A brace is added to a tree house as shown. Explain why the brace is not parallel to the floor. Image taken from: Geometry. McDougal Littell: Boston, P. 389.
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Theorem 8.6: If three parallel lines intersect two transversals, then they divide the transversals proportionally. Image taken from: Geometry. McDougal Littell: Boston, P. 398.
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Theorem 8.7: 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. Image taken from: Geometry. McDougal Littell: Boston, P. 398.
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Ex. 3. Using the information in the diagram, find the distance between First Street and Main Street.
Image taken from: Geometry. McDougal Littell: Boston, P. 399.
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Ex. 3. Using the information in the diagram, find the distance between First Street and Main Street.
Answer: 510 m Image taken from: Geometry. McDougal Littell: Boston, P. 399.
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Ex.4 Image taken from: Geometry. McDougal Littell: Boston, P. 391.
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Ex.4 Answer: 22 6/7 Image taken from: Geometry. McDougal Littell: Boston, P. 391.
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8.6, p. 502, #3-14 all, all (20 questions)
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