Detour Proofs and Midpoints

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Presentation transcript:

Detour Proofs and Midpoints Modern Geometry Section 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 . A C

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

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:

Finding the Coordinates of a Midpoint The Midpoint Formula is:

Finding the Coordinates of a Midpoint The Midpoint Formula is:

One more for the road…