Question

given a line segment AB and a point C not on it, using appropriate axiom there is only one perpendicular point fron C on AB ​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

Given,

A line segment AB and a point C

Required to prove

There is only one perpendicular point from A on AB

Proof

Let D is a point on the line AB such that CD is perpendicular to AB.

∠CDA = 90°

We need to prove that there is only one perpendicular that can be drawn from CD to AB.

Let us assume the contradiction.

Then there exists another point E other than D on AB such that CE is perpendicular to AB

That is ∠CEA = 90°

That ∠CDA =  ∠CEA, which is possible only when D and E are the same points.

That is CD and CE are the same lines.

Hence It is proved that there is only one perpendicular can be drawn from an external point C to the line segment.

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