Warm Up  Sit in the same seats as yesterday  Put your puzzle pieces together  Use glue sticks on round table  Use marker to go over the answers if you are having trouble seeing them!

Opener: A T F B N Given: AT || BN FA = 12, FT = 15 AT = 14, AB = 8 Find: length BN & NT Label sides

Prove similar triangles first = =

Answer:  BN = 23 1/3  TN = 10

B E A C D T65: If a line is || to one side of a Δ and intersects the other 2 sides, it divides those 2 sides proportionally. (Side splitter theorem) 8.5 Three Theorems Involving Proportions Given: BE  CD Prove: =

B E A C D ∆ABE ~ ∆ACDAA ~ = = If a line is parallel to one side, it divides the 2 sides proportionally. Substitute: addition of two segments AE(AB+BC) = AB(AE+ED) NOW:Cross multiply AE  AB+AE  BC=AB  AE+AB  ED Proof of T65

AE  BC = AB  ED Subtract AB  AE = Ratio of top side to bottom side.

Given: AT  BN FA = 6, FT = 3, AT = 5, TN = 4 Find: length BN and AB A T F B N Remember to label the shape and set up proportions using corresponding sides or side splitter theorem.

Answer:  BN = 35/3  AB = 8

T66: If three or more parallel lines are intersected by two transversals, the parallel lines divide the transversals proportionally. AB C E D F G Given: AB CD EF Conclusion:    = Draw AF

In Δ EAF,= In Δ ABF,= Substitute BD for AG and DF for GF, substitution or transitive =

T67: If a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the adjacent sides. (Angle Bisector Theorem) D C B A Given: ∆ ABD AC b <BAD Prove: =  =

Set up Proportions = BC AD = AB CD Means Extreme Therefore: = = =

Given <ABD <DBC Lengths as shown Find: DC A B CD Set up segment proportions first then fill in numbers. = X = 5

a G ZS Y I P X W b c d Given: a, b, c and d are parallel lines, Lengths given WZ = 15 Find: WX, XY and YZ