Warmup!:

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)

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

Proof of side-splitter thm B C G D F 1.) m<C=m<C1.) Given 2.) m<CDF=m<CGB2.) “ “ 3.) ∆CDF~∆CGB3.) AA 4.) x-y=z4.) seg. Sub. 5.) r-t=w5.) “ “ 6.) x = r6.) def. similar y t 7.) x -1 = r -17. Subtr. Prop. y t 8.) x - y = r – y8.) subs. y y y y9.)10.) y t x r z w Prove that z/y=w/t

Examples x x x 10

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

Examples 5 7 x x 24 - x

Theorem 7-5 Triangle Angle-Bisector Theorem If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides. If DG bisects  FDE then GF D E Proof: riangle-properties/angle_bisectors/v/angle- bisector-theorem-proof riangle-properties/angle_bisectors/v/angle- bisector-theorem-proof

Examples x x x 6

Tonight’s homework: pg