4 1 Detours Midpoints Obj Use detours in

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 B D Prove: ABE ADE Do we have enough info? C We only have sides AB AD & AE We need an angle.

EX. 1 cont. Prove ABC ADC First by SSS Statements 1. 2. 3. 4. 5. 6. 7. (S) AB AD (S) BC DC (S) AC ABC ADC (A) BAC DAC (S) AE ABE ADE Reasons 1. 2. 3. 4. 5. 6. 7. Given Reflexive Property SSS (1, 2, 3) CPCTC Reflexive Property SAS (1, 5, 6)

Procedure for Detour Proofs 1. Determine which triangles you must prove to be congruent to reach the required conclusion. 2. Attempt to prove that these triangles are congruent. If you cannot do so for lack of enough information, take a detour. 3. Identify the parts that you must prove to be congruent to establish the congruence of the

Procedure for Detour Proofs 4. Find a pair of triangles that 1. You can readily prove to be congruent. 2. Contain a pair of parts needed for the main proof. 5. Prove that the triangles found in step 4 are congruent. 6. Use CPCTC and complete the proof planned in step 1.

Midpoint formula: for the midpoint of a line take the average of two given points. Xm = X 1 + X 2 2 EX. 2: Find the midpoint of line segment AB X = -2 + 8 A B X 2 3 -2 8 equal distance, hence midpoint =6 2 =3

Midpoint formula for segment on the coordinate plane: • Find the midpoint of (1, 4) and (6, 2). • 1 + 6, 4 + 2 2 2 ( • (7 / 2 , 6 / 2 ) • (3. 5, 3) )