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Detour Proofs and Midpoints
Modern GeometrySection 4.1
Detour Proofs In some proofs it
is necessary to prove more than one pair of triangles congruent
We call these proofs Detour Proofs
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
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
Yet another bad comic…
Midpoint of a Segment
The midpoint of a segment is the point that divides, or bisects, the segment into two congruent segments.
Midpoint on the Number Line Find the midpoint
of AC
. .A C
Midpoint on the Number Line Find the midpoint
of BD
. .B D
Finding the Coordinates of aMidpoint If you know the endpoints of a
segment, you can use the Midpoint Formula to find the midpoint.
The Midpoint Formula is:
Finding the Coordinates of aMidpoint The Midpoint Formula is:
Finding the Coordinates of aMidpoint The Midpoint Formula is:
One more for the road…