Geometry Congruence and Bisectors

[rpursellusa]

Error Analysis

YP=68 m. MP=68 m.

Noticing this, you conclude that point P is the midpoint of YM. Why is this not necessarily correct?

 

[Deleted member 4993]

Error Analysis

YP=68 m. MP=68 m.

Noticing this, you conclude that point P is the midpoint of YM. Why is this not necessarily correct?

For your conclusion to be true, the condition is:

|YP| + |MP| = |YM|

 

[Ishuda]

As Subhotosh Khan implied, Y, M, P must be co-linear for this to be true. However you could note that the set of P such that YP = MP is the perpendicular bisector of YM.