Question

if AM=MB, then M is the midpoint of segment AB. true or false for logical reasoning (if-then statements) in geometry.

Answer 1

Answer:

FALSE (in general)

Step-by-step explanation:

Consider an equilateral triangle T with vertices A, B and M.

Since T is a triangle, then A,B and M are not collinear (they are not in the same line).  

As T is equilateral, then AM =MB.

If M were the midpoint of AB, then M would lie on the same line that joins A and B, so A,B and M would be collinear, which is a contradiction.

So M cannot be the midpoint of AB.