I don't understand how this statement is true:

If AB = BC then B is the midpoint of AC

Do you know what the midpoint is? It is the point midway between A and C. That is, it is the same distance from A as it is from C.

That is, AB = BC

Well, let me explain it with a bit of humor!

Imagine we're talking about food instead of algebra. Let's say you have a pizza, and you cut it into three equal slices. If you label those slices as AB, BC, and AC, and AB happens to be the same size as BC, that means the second slice is in the middle, right?

So, in this case, if AB = BC, we can conclude that B is the midpoint of AC. Just like the middle slice of pizza is in the middle of the whole pizza!

I hope that helps you understand the concept a little better, and now you're probably craving some pizza, aren't you?

To understand why the statement is true, let's break it down step-by-step:

Step 1: Understanding the statement
The statement says, "If AB = BC, then B is the midpoint of AC." It is talking about a triangle ABC, where AB and BC are two sides of the triangle.

Step 2: Definition of a midpoint
In geometry, the midpoint of a line segment is a point that divides the segment into two equal parts. So, if B is the midpoint of AC, it means that AB and BC are equal in length.

Step 3: Understanding the equality AB = BC
If AB = BC, it means that the lengths of the line segments AB and BC are equal. In other words, the distance from point A to point B is the same as the distance from point B to point C.

Step 4: Visualizing the situation
To better understand this concept, you can draw a triangle ABC on a piece of paper. Let's assume AB is equal to BC. Draw a segment AB and label its length as x. Then, draw segment BC with the same length x.

Step 5: Checking if B is the midpoint of AC
Now, draw another segment AC such that B lies on AC. Since AB = BC, this means that B is equidistant from both A and C.

Step 6: Conclusion
Based on our visualization, since B is equidistant from both A and C, it satisfies the definition of a midpoint. Therefore, if AB = BC, then B is indeed the midpoint of AC.

In summary, if you have a triangle ABC, and AB is equal to BC, then B is the midpoint of AC because it divides the segment AC into two equal parts.

To understand why the statement is true, let's explore what it means for B to be the midpoint of AC.

When we say that B is the midpoint of AC, it means that B divides the line segment AC into two equal parts. In other words, the distance from A to B is the same as the distance from B to C.

Now, let's consider the statement "If AB = BC."

If AB = BC, it means that the length of the line segment AB is equal to the length of the line segment BC.

If we connect A and C with a line segment and B lies on that line segment, and AB = BC, then B must be exactly halfway between A and C. This is because if AB and BC have the same length, it implies that B is equidistant from A and C. Therefore, B is the midpoint of AC.

To visualize this, you can draw a line segment AC and label points A and C. Then, if AB = BC, you can draw the line segment AB and extend it to meet the line segment AC. The point at which AB intersects AC will be the point B, which verifies that B is the midpoint of AC.

So, if AB = BC, then B is the midpoint of AC.