1 / 21

6.4 Parallel Lines and Proportional Parts 6.5 Parts of Similar Triangles

6.4 Parallel Lines and Proportional Parts 6.5 Parts of Similar Triangles. First & Last Name February 26, 2014 ______Block.

pandora-farmer
Download Presentation

6.4 Parallel Lines and Proportional Parts 6.5 Parts of Similar Triangles

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. 6.4 Parallel Lines and Proportional Parts6.5 Parts of Similar Triangles First & Last Name February 26, 2014 ______Block

  2. Triangle Proportionality Theorem: If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it separates these sides into segments of proportional lengths.

  3. 1. In △EFG, and . Find LG.

  4. Converse of the Triangle Proportionality Theorem: If a line intersects two sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the third side.

  5. 2. In △HKM, is twice the length of . Determine whether .

  6. A midsegment of a triangle is a segment whose endpoints are the midpoints of two sides of the triangle. • Triangle Midsegment Theorem: A midsegment of a triangle is parallel to one side of the triangle, and its length is one-half the length of that side.

  7. 3. Triangle ABC has vertices A(-4, 1), B(8, -1), and C (-2, 9). is a midsegment of △ABC. a. Find the coordinates of D and E.

  8. Verify that is parallel to • Verify that

  9. Corollary 6.1: If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally. • Corollary 6.2: If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

  10. 4. Find EF if AC=16, BC=10, and DF=20.

  11. 5. Find x and y.

  12. Proportional Perimeters Theorem: If two triangles are similar, then the perimeters are proportional to the measures of corresponding sides.

  13. 6. If △LMN ~ △QRS, QR=35, RS=37, SQ=12, and NL=5, find the perimeter of △LMN.

  14. 7. Find the perimeter of △WZX, if △WZX~△SRT, ST=6, WX=5, and the perimeter of △SRT=15.

  15. Theorems: If two triangles are similar, then the measures of the corresponding altitudes, angle bisectors, and medians are proportional to the measures of corresponding sides.

  16. 8. Find x.

  17. 9. In the figure, △ABC~△DEF. is a median of △ABC and is a median of △DEF. Find EH if BC=30, BG=15, and EF=15.

  18. 10. The drawing below illustrates the position of the camera and the distance from the lens of the camera to the film. Find the height of the sculpture.

  19. Angle Bisector Theorem: An angle bisector in a triangle separates the opposite side into segments that have the same ratio as the other two sides.

  20. 11. Find x.

  21. Exit Slip • Find the perimeter of △DEF. • Find x. • Use the figure below. • If RL=5, RT=9, and WS=6, find RW. • If TR=8, LR=3, and RW=6, find WS. • Find x and y.

More Related