1 / 9

6.4 Parallel Lines and Proportional Parts

6.4 Parallel Lines and Proportional Parts. What you’ll learn: To use proportional parts of triangles To divide a segment into parts. Theorem 6.4. Triangle Proportionality Theorem

tillie
Download Presentation

6.4 Parallel Lines and Proportional Parts

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 Parts What you’ll learn: To use proportional parts of triangles To divide a segment into parts.

  2. Theorem 6.4 Triangle Proportionality Theorem If a line is parallel to one side of a triangle and intersects the other 2 sides in 2 distinct points, then it separates these sides into segments of proportional parts. If BC  DE, then A B C D E

  3. Theorem 6.5 Converse of the Triangle Proportionality Theorem If a line intersects 2 sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the 3rd side. If then BCDE. A B C D E

  4. The midsegment of a triangle is a segment whose endpoints are the midpoints of 2 sides of the triangle. Theorem 6.6 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. If B is a midpoint of AD and C is a midpoint of AE, then BCDE and BC=½DE A B C D E

  5. Corollaries 6.1 If 3 or more parallel lines intersect 2 transversals, then they cut off the transversals proportionally. 6.2 If 3 or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal. If AB=BC, then DE=EF A D B E C F A D B E C F

  6. In RST, RTVU, SV=3, VR=8, UT=12. Find SU 8x=36 SU=4½ R 8 V 3 S x U 12 T

  7. In DEF, DH=18, HE=36, and DG=½GF. Determine whether GHFE. Explain ½x36=18x 18x=18x yes, segments are proportional. D 18 ½x H G 36 x E F

  8. Find x. 33 1. 11(x+12)=22x 11x+132=22x 132=11x x=12 2. x=23.5 x 11 x+12 x 47

  9. Homeworkp. 31214-34 even50-56 even

More Related