Question

If a point P be the midpoint of a line segment AB,then prove that AP=BP=1/2AB

Answer 1

As P is the midpoint to line segment AB, the midpoint divides the line segment into two equal parts ie AP=BP=1/2AB.
AB=AP+BP
since AP=BP therefore
AB=2APor AB=2BP
AP=1/2AB

Answer 2

Answer:

$AP=BP=\frac{1}{2}AB=AP$

Step-by-step explanation:

Given information: Point P be the midpoint of a line segment AB.

To prove: AP=BP=1/2AB

Proof:

It is given that point P be the midpoint of a line segment AB. It measn point P divides the line AB in two equal parts AP and BP.

$AP=BP$               .... (1)

Using segment addition property, we get

$AB=AP+PB$

$AB=AP+BP$

Using equation (1) we get

$AB=AP+AP$

$AB=2AP$

Divide both sides by 2.

$\frac{1}{2}AB=AP$         .... (2)

Using (1) and (2) we get

$AP=BP=\frac{1}{2}AB=AP$

Hence proved.