detour proofs and midpoints modern geometry section 4.1

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…