1. 4.1 Detours & Midpoints Test will be handed out after lesson. Obj: Use detours in proofs Apply the midpoint formulas Apply the midpoint formulas

2. Warm Up

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

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

5. 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

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

7. The End