1. Detour Proofs and Midpoints
Modern Geometry
Section 4.1

2. Detour Proofs
In some proofs it is necessary to prove more than one pair of triangles congruent
We call these proofs Detour Proofs

3. Detour Proofs Procedure for Detour Proofs
Determine which triangles you must prove congruent to reach the desired conclusion
Attempt to prove those triangles congruent – if you cannot due to a lack of information – it’s time to take a detour…
Find a different pair of triangles congruent based on the given information
Get something congruent by CPCTC
Use the CPCTC step to now prove the triangles you wanted congruent

4. Detour Proofs
To summarize: In detour proofs we prove one pair of triangles congruent, get something by CPCTC, and use that to prove what we were asked to prove in the first place

5. Yet another bad comic…

6. Midpoint of a Segment
The midpoint of a segment is the point that divides, or bisects, the segment into two congruent segments.

7. Midpoint on the Number Line
Find the midpoint of . A C

8. Midpoint on the Number Line
Find the midpoint of . B D

9. Finding the Coordinates of a Midpoint
If you know the endpoints of a segment, you can use the Midpoint Formula to find the midpoint.
The Midpoint Formula is:

10. Finding the Coordinates of a Midpoint
The Midpoint Formula is:

11. Finding the Coordinates of a Midpoint
The Midpoint Formula is:

12. One more for the road…