1 / 20

6.6 Use Proportionality Theorems

6.6 Use Proportionality Theorems. Objectives. Use proportional parts of triangles Divide a segment into parts. Triangle Proportionality Theorem.

linh
Download Presentation

6.6 Use Proportionality Theorems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 6.6 Use Proportionality Theorems

  2. Objectives • Use proportional parts of triangles • Divide a segment into parts

  3. Triangle Proportionality Theorem • Theorem 6.4If a line is parallel to one side of a Δ and intersects the other two sides in two distinct points, then it separates these sides into segments of proportional lengths. EG=EHGDHF *The Converse of the Δ Proportionality Theorem is also true.

  4. In and Find SU. S From the Triangle Proportionality Theorem, Example 1:

  5. Answer: Example 1: Substitute the known measures. Cross products Multiply. Divide each side by 8. Simplify.

  6. In and Find BY. B Your Turn: Answer: 15.75

  7. In and Determine whether Explain. Example 2:

  8. In order to show that we must show that Since the sides have proportional length. Answer: since the segments have proportional lengths, Example 2:

  9. In andAZ = 32. Determine whether Explain. X Answer: No; the segments are not in proportion since Your Turn:

  10. What does the Δ Proportionality Theorem Also Tell Us • The Δ Proportionality Theorem has shown us that || lines cut the sides of a Δ into proportional parts. Three or more parallel lines also separate transversals into proportional parts.

  11. Additional Theorems • Theorem 6.6 If 3 or more || lines intersect 2 transversals, then they divide the transversals proportionally. • AB = DE BC EF A D E B C F

  12. Additional Theorems • Theorem 6.7 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. • PT = TS PU US T P U S

  13. Example 3: In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x.

  14. Example 3: Notice that the streets form a triangle that is cut by parallel lines. So you can use the Triangle Proportionality Theorem. Triangle Proportionality Theorem Cross products Multiply. Divide each side by 13. Answer: 32

  15. Your Turn: In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x. Answer: 5

  16. Example 4: Find x and y. To find x: Given Subtract 2x from each side. Add 4 to each side.

  17. The segments with lengths are congruent since parallel lines that cut off congruent segments on one transversal cut off congruent segments on every transversal. Example 4: To find y:

  18. Example 4: Equal lengths Multiply each side by 3 to eliminate the denominator. Subtract 8y from each side. Divide each side by 7. Answer: x = 6; y = 3

  19. Your Turn: Find a and b. Answer: a = 11; b = 1.5

  20. Assignment • Geometry Workbook Pgs. 118 – 119 #1 – 25

More Related