Question

Segments proofs. B is the midpoint of AC Prove 2bc=AB

Answer 1

In the context of B being the midpoint of AC, the proof demonstrates that
`\(2 \cdot BC\)` equals AB, highlighting the relationship between the segments in a scenario where B is the midpoint.

In the given scenario where B is the midpoint of AC, we aim to prove that
`\(2 \cdot BC = AB\)`.

By the definition of a midpoint, BC is equal to BA (segment addition postulate).

Now, considering the entire segment AC, which is composed of two equal parts (AB and BC), we can express AC as
`\(2 \cdot BC\)`.

Substituting the earlier established equality BC = BA into this expression, we get
`\(2 \cdot BA\)`, which is equivalent to AB.

Thus,
`\(2 \cdot BC = AB\)`, confirming the assertion that in a segment where B is the midpoint, the double of one of its segments equals the other segment.

Answer 2

B is the midpoint of AC because <AB and <BC have the same measurement.