Question

if point. c lies between two points a to b such that ac=bc the prove that ac=1/2 ab explain by drawing the figure​

Answer 1

Answer:-

★ Given:-

AC = BC

★ Now, adding AC both sides.

L.H.S + AC = R.H.S + AC

AC + AC = BC + AC

2AC = BC + AC

★ We know that,

BC + AC = AB

(As it coincides with line segment AB, from figure)

Therefore, 2 AC = AB

(If equals are added to equals, the wholes are equal)

→ AC = 1/2 AB

Hence proved!

Answer 2

Given :-

Point C lies between two points A and B, such that AC = BC.

To prove :-

AC = 1/2 AB, or, C is the mid-point of AB.

Proof :-

METHOD - 1 :-

AC = BC        (given)          ...(i)

AC + BC = AB   (given)

From eq. (i),

AC + AC = AB

⇒2 AC = AB

⇒AC = AB/2

⇒AC = 1/2 AB

METHOD - 2 :-

In eq.(i), adding AC to both sides :-

AC + AC = BC + AC

⇒2 AC = AB             (As C lies between AB, so BC + AC = AB)

⇒AC = AB/2

⇒AC = 1/2 AB

HENCE PROVED.