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