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Chapter 7: Similarity

Chapter 7: Similarity. Section 7-5: Proportions in Triangles. Objectives. To use the side-splitter theorem. To use the triangle angle-bisector theorem. Theorem 7-4: “The Side-Splitter Theorem”.

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Chapter 7: Similarity

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  1. Chapter7: Similarity Section 7-5: Proportions in Triangles

  2. Objectives • To use the side-splitter theorem. • To use the triangle angle-bisector theorem.

  3. Theorem 7-4:“The Side-Splitter Theorem” • If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

  4. Using the Side-Splitter Theorem • Solve for x.

  5. Using the Side-Splitter Theorem • Solve for x.

  6. Corollary to Theorem 7-4: • If three parallel lines intersect two transversals then the segments intersected on the transversals are proportional.

  7. Example: • Solve for x.

  8. Example • Solve for x.

  9. Theorem 7-5:“Triangle Angle Bisector Theorem” • If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

  10. Using the Triangle Angle Bisector Theorem • Solve for x

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