Q4 of 9 Page 85

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

Here,


AC = BC



Now,


After adding AC both side, we get


AC + AC = BC + AC


 


2AC = AB (Since, If equals are added to equals, the wholes are equal.)


 


Therefore,


AC = AB

More from this chapter

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2

Give a definition for each of the following terms. Are there other terms that need to be defined first? What are they, and how might you define them?

(i) Parallel lines


(ii) Perpendicular lines


(iii) Line segment


(iv) Radius of a circle


(v) Square

 3

Consider two ‘postulates’ given below:

(i) Given any two distinct points A and B, there exists a third point C which is in between A and B.


(ii) There exist at least three points that are not on the same line.


Do these postulates contain any undefined terms? Are these postulates consistent?


Do they follow from Euclid’s postulates? Explain.

 5

In Question 4, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.

 6

In Fig. 5.10, if AC = BD, then prove that AB = CD.