4.1 Detours & Midpoints. Obj: Use detours in proofs Apply the midpoint formulas. 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
Obj: Use detours in proofs
Apply the midpoint formulas
A E Given: AB AD
B D Prove: ABE ADE
Do we have enough info?
We only have sides AB AD & AE AE
We need an angle.
Determine which triangles you must prove to be congruent to reach the required conclusion.
Attempt to prove that these triangles are congruent. If you cannot do so for lack of enough information, take a detour.
Identify the parts that you must prove to be congruent to establish the congruence of the triangles.
X = -2 + 8 2
= 6 2
EX.2: Find the midpoint of line segment AB
equal distance, hence midpoint
Find the midpoint of (1, 4) and (6, 2).
1 + 6, 4 + 2 2 2