Warmup !:

1. Warmup!:

2. Extra credit opportunity! Proving corollary from chp. 7 (3 points) Don’t need statement/reason proof, just algebra (hint use similar triangles, not pythagorean theorem)

3. Theorem 7-4 Side-Splitter Theorem G If GB // DF, then D B F C If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.

4. G D B F C Proof of side-splitter thm Prove that z/y=w/t 1.) m<C=m<C 1.) Given 2.) m<CDF=m<CGB 2.) “ “ 3.) ∆CDF~∆CGB 3.) AA 4.) x-y=z 4.) seg. Sub. 5.) r-t=w 5.) “ “ 6.) x = r 6.) def. similar y t 7.) x -1 = r -1 7. Subtr. Prop. yt 8.) x - y = r – y 8.) subs. y y y y 9.) 9.) 10.) 10.) z x y w t r

5. Examples 6 x 12 x 14 10 3 1 14 - x

6. Corollary to Theorem 7-4 If three parallel lines intersect two transversals, then they divide the transversals proportionally. If AD // BF // CG, then A D B F G C

7. Examples x 5 9 7 x 9 24 - x 18

8. Theorem 7-5 Triangle Angle-Bisector Theorem If DG bisects ÐFDE then F G E D If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides. Proof: http://www.khanacademy.org/math/geometry/triangle-properties/angle_bisectors/v/angle-bisector-theorem-proof

9. Examples 8 14 x 21 6 9 x 10 - x

10. Tonight’s homework: pg 400-401 1-24