Question

If a point C lies between two points A and B such that AC = BC, then prove that AC =1/2 AB.

Answer 1

Answer:

Solution:

Given, AC = BC

Now, add AC on both sides.

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

AC + AC = BC + AC

2AC = BC + AC

Since, we know,

BC +AC = AB (as it coincides with line segment AB, from figure)

∴ 2 AC = AB (If equals are added to equals, the wholes are equal.)

⇒ AC = 1/2 AB.

Hope it will be helpful :)

Answer 2

Answer:

given:-line segmentA B having mid point c such that AC=BC

to proove:- AC=1/2AB

proof:-AC=BC (GIVEN) EQUATION 1

AC+BC=AB (GIVEN THAT C IS THE MID POINT OF AB) EQUATION 2

from equation one and two we get

AC+AC=AB

2AC=AB

AC=1/2AB