Obj: Use detours in proofs Apply the midpoint formulas 4.1 Detours & Midpoints Obj: Use detours in proofs Apply the midpoint formulas

Warm Up

Detour Proofs: used when you need to prove 2 pairs of ’s = to solve a case. Ex:1 A E Given: AB = AD BC = CD B D Prove: ABE = ADE Do we have enough C info? We only have sides AB = AD & AE = AE We need an angle

Prove ABC = ADC First by SSS EX.1 cont. Prove ABC = ADC First by SSS Statements (S) AB = AD (S) BC = DC (S) AC = AC ABC = ADC (A) BAC = ADC (S) AE = AE ABE = ADE Reasons Given Reflexive Property SSS (1,2,3) CPCTC SAS (1,5,6) ~ ~ ~ ~ ~ ~ ~

Midpoint formula: for the midpoint of a line: X = X + X Take the average of two given points EX.2: Find the midpoint of line segment AB A X B X = -2 + 8 = 6 equal distance = 3 hence midpoint

Midpoint formula for segment on the coordinate plane: EX.3 Find mdpt. of segment (1, 4) (6, 2) (x, y) (x , y ) Ans: m (xm, ym ) = 1+6 , 4+2 = 7 , 6 = 7 ,

The End