8.6: Proportions and Similar Triangles

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Proportions and Similar Triangles

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Presentation transcript:

8.6: Proportions and Similar Triangles GEOMETRY: Chapter 8 8.6: Proportions and Similar Triangles

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, 2007. P. 397.

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, 2007. P. 397.

Ex. 1: Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 398.

Ex. 1: Answer: 9 Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 398.

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, 2007. P. 389.

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, 2007. P. 389.

Theorem 8.6: If three parallel lines intersect two transversals, then they divide the transversals proportionally. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 398.

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, 2007. P. 398.

Ex. 3. Using the information in the diagram, find the distance between First Street and Main Street. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 399.

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, 2007. P. 399.

Ex.4 Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 391.

Ex.4 Answer: 22 6/7 Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 391.

8.6, p. 502, #3-14 all, 21-28 all (20 questions)