Q33 of 66 Page 91

A point C lies between two points A and B such that AC=CB. Prove that AC=AB.

According to question, C lies between points A and B and AC = BC



Adding AC both side we get,


AC + AC = BC + AC


According to definition of Euclid, if equals are added to equals, whole will equal.


Here, (BC + AC) will coincides with AB.


2AC = AB


So, AC = AB


More from this chapter

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31

Match the following columns:











Column I



Column II



(a)A line segment has a


(b) A ray has the end point


(c) How many lines can be drawn to pass through a given point?


(d) How many lines can be drawn to pass through two given points?



(p) Infinitely many


(q) definite length


(r) B


(s) Only one



The correct answer is:


(a)-………, (b)-……., (c)-…….., (d)………

 32

Fill in the blanks (2 marks)

(A) Concurrent lines………through a given point.


(B) Two distinct………in a plane cannot have more than one point in common.


(C) Two distinct points in a plane determine a………line.


(D) A line segment has…….end points.

 34

Prove that every line segment has a unique mid-point.

 35

In the given figure, AC=BD.

Prove that AB=CD.