Q17 of 22 Page 5

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

Here,


AC = BC



Now,


After adding AC both sides, we get


AC + AC = BC + AC


(Since, if equals are added to equals, the wholes are equal.)


2AC = AB


Therefore,


AC = 1/2 AB


Hence Proved


More from this chapter

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15

In the Fig, if OX = 1/2 XY, PX = 1/2 XZ and OX = PX, show that XY = XZ.

 16

In the Fig,

(i) AB = BC, M is the mid-point of AB and N is the mid- point of BC. Show that AM = NC.
(ii) BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that AB = BC.


 18

In Fig., if AC = BD, then prove that AB = CD.

 19

A point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.