Question

If B lies on line AC and points A, B and C are distinct such that, AB + BC = AC, then

A.
AB < AC


B.
AB > AC


C.
AB = AC


D.
None of these

Answer 1

Hey there !!

⨷ Answer ➣ Option A ) AB <AC

Explanation -

Here suppose ABC is the line Given that

In Option

B ) Which states AB> AC , it is not possible because AB + BC = AC , as AC is Greater and AB And BC By sum to make equal with AC


C) AB = AC
It isn't an Desired answer because AB ≠ AC
if it would have then AB + BC = AC



Hence Option A is right one


Hope this would help you !!

Answer 2

HELLO DEAR,

WE SOMETIMES WILL WRITE A-B-C, WHICH MEANS "B IS BETWEEN A AND C."

THE DEFINITION USES DISTANCE

, AND APPLYING THE CONCEPT OF A

COORDINATE SYSTEM WE HAVE THE

FOLLOWING THEOREM.

BY THE RULER POSTULATE:

AB = |y-x|

BC = |z-y|

AC = |z-x|.

BUT y-x IS POSITIVE BECAUSE x < y; SIMILARLY, z-y AND z-x ARE POSITIVE. SO:

AB = y-x

BC = z-y

AC = z-x

FINALLY:
AB + BC = (y - x) + (z - y)
= z-x
=AC.

SINCE AB + BC = AC, A-B-C BY THE DEFINITION OF BETWEEN.


AND HENCE,
AB<AC

I HOPE ITS HELP YOU DEAR,
THANKS