If a point C lies between two points A and B such that AC = BC, then prove that AC = $\frac{1}{2}$ AB. Explain by drawing the figure.

Question

If a point C lies between two points A and B such that AC = BC, then prove that AC =  $\frac{1}{2}$  AB. Explain by drawing the figure.

cdquestions Admin · Accepted Answer

It is given that,  AC = BC AC+AC= BC + AC        (Equals are added on both sides) … (1)  Here, (BC + AC) coincides with AB. It is known that things which coincide with one another are equal to one another.  ∴ BC + AC = AB … (2)  It is also known that things which are equal to the same thing are equal to one another. Therefore, from equations (1) and (2), we obtain  AC + AC = AB  2AC = AB ∴ AC =  $\frac{1}{2}$  AB

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

If a point C lies between two points A and B such that AC = BC, then prove that AC = \(\frac{1}{2}\) AB. Explain by drawing the figure.

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions