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

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Solution

Draw a line segment with the given statement.
Consider the line $A B$ , where point $C$ is at the intersection of $A$ and $B$ :
Since $C$ is the point between $A$ and $B$
Assume $A B = 10 cm$ such that $C B = 6 cm and A C = 4 cm$ it is as follows:
$\begin{array}{rcl} A C + C B & = & 6 + 4 \\ \Rightarrow & A C + C B = 10 \\ \Rightarrow & A C + C B = A B \end{array}$

Hence, the line segment is and $A B = A C + C B$ .

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

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

A point C is called the midpoint of a line segment $¯ ¯¯¯¯¯¯ ¯ A B$ if

(a) C is an interior of AB

(b) AC=CB

(d) AC+CB=AB

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

Draw a line segment with the given statement.Consider the line AB, where point C is at the intersection of A and B:Since C is the point between A and BAssume AB=10cm such that CB=6cmandAC=4cm it is as follows: AC+CB=6+4⇒AC+CB=10⇒AC+CB=ABHence, the line segment is and AB=AC+CB.

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