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Point C is the mid-point of line segment AB, prove that every

Question

Point $C$ is the mid-point of line segment $A B$ , prove that every line segment has one and only one mid-point.

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Point

C

is the mid-point of line segment

A B

, prove that every line segment has one and only one mid-point.

15 mins ago

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Text solutionVerified

A C = BC

...

(i)

If possible, let

D

be another mid-point of

A B

A D = D B

...

(ii)

Subtracting

(ii)

from

(i)

A C - A D = BC - D B

D C = - D C

(∵ A C - A D = D C an d CB - D B = - D C)

D C + D C = 0

2 D C = 0

D C = 0

So,

C

and

D

coincide.

Thus, every line segment has one and only one mid-point.

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Question Text	Point $C$ is the mid-point of line segment $A B$ , prove that every line segment has one and only one mid-point.
Answer Type	Text solution:1
Upvotes	150