Point M is the midpoint of line ABMC. Which of the following statements is NOT true? Why?

(1)AM=MC
(2)AB <MC
(3)AM >BC
(4)BM <MC

AM > BC

The statement that is NOT true is (4) BM < MC.

According to the definition of a midpoint, point M is exactly in the middle of line AB. This means that AM is equal to MC, which makes statement (1) true.

Since point M is the midpoint of line AB, it is also a point on line AB. So, the length of AB must be greater than the length of MC. Therefore, statement (2) AB < MC is false.

Statement (3) AM > BC can be true or false depending on the specific lengths of the line segments. Without further information about the lengths of each segment, we cannot determine its truth value.

Finally, statement (4) BM < MC is false. Since point M is the midpoint of line AB, BM and MC are equivalent line segments, making them equal in length.

Therefore, the correct answer is (4) BM < MC.

To determine which of the given statements is NOT true, we can apply the midpoint property. According to the midpoint property, in a line segment, the line segment is divided into two equal halves at the midpoint.

In this case, point M is the midpoint of line ABMC, which means that M divides the line segment into two equal halves. Let's analyze each statement:

(1) AM=MC: This statement is true because M is the midpoint of ABMC, so the distance from A to M is equal to the distance from M to C.

(2) AB < MC: This statement could be true or false depending on the specific lengths of AB and MC. We cannot determine its truth value without additional information, so we cannot conclude that this statement is NOT true.

(3) AM > BC: This statement is false because the distance from A to M cannot be greater than the distance from B to C. Since M is the midpoint, it divides the line segment into two equal parts, and AM is equal to MC, meaning that both are shorter than BC.

(4) BM < MC: This statement is true because whenever a point (in this case, M) divides a line segment (in this case, AB) into two parts, the distance from that point to one end of the line segment (BM) is always shorter than the distance from that point to the other end (MC).

Therefore, the statement that is NOT true is (3) AM > BC.

A and C are the ends of the line.

If M is at the midpoint, AM = MC

It does not matter where B is.