If $A, B$ and $C$ are three points on a line, and $B$ line between $A$ and $C$ (see fig.) , then prove that $A B + B C = A C$

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Solution

Let $A B = x$
and
$B C = y$
Let $‘ D^{'}$ be a reterm is part such that
$\to A B = \to D B - \to D A$
Now, $\to A B = \to D B - \to D A - - - - - (1)$
Similarly, $\to B C = \to D C - \to D B - - - - - (2)$
$(1) + (2)$
$\to A B + \to B C = \to O B - \to O A + \to O C - \to O B$
$\to A B + \to B C = \to O C - \to O A$
$\to A B + \to B C = \to A C$

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Similar questions

A, B, C

B

A

C

A C - A B = B C

A B + B C = A C

Draw any line segment, say. Take any point C lying in between A and B. Measure the lengths of AB, BC and AC. Is AB = AC + CB?

[Note: If A, B, C are any three points on a line such that AC + CB = AB, then we can be sure that C lies between A and B]

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