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

4. 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) ~ ~ ~ ~ ~ ~ ~

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 =
= 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 (xm, ym ) = 1+6 , 4+2
= 7 , 6
= 7 ,

7. The End