Segments which share a common endpoint must be perpendicular?

Question

Segments which share a common endpoint must be perpendicular?

True or False

You must give some support to your answer to back it up.

Answer 1

true, in the euclidian space DEFINED by these 2 segments, the 2 segments are perpendicular

(i'm redefining "perpendicular" to suit my answer... which I am allowed to do...)

Answer 2

Normally it is false but true in some special cases.

I am giving you a simple small example to understand this phenomena.

Consider the wall-clock. Assume that the houra hand and minutes hand are two line segments which have the common points at the centre of the clock.

Consider the time in the watch to be 2'Oclock. Now the angle between the two hands will roughly be 60 - 70 degrees. And they are called perpendicular if they have the angle between them as 90 degrees. For more transparency, consider the time to be 4'O clock. Then also the 2 lines will not be perpendicular.

As I said to you earlier that "Normally it is false but true in some special cases", the special cases are 3'O clock and 9'O clock. So you statement will be true only in some cases.

Hope you can understand this clearly.

Answer 3

Not true. Only segments which meet at a right angle are perpendicular. An infinite number of angles exist at which two segments may meet to share a common endpoint, but are not perpendicular. For example, two segments meeting at a 45-degree angle share a common endpoint, but are certainly not perpendicular.

Answer 4

False, think of a triangle. It is made of three line segment, that have a common endpoint with both of the other segments. That means that there are 3 angles. Since the sum of the angles of a triangle is π radians, they must have an average angle of π/3 radians. Thus they cannot all be perpendicular to each other.

Answer 5

The word 'Must', no, it's not must.

If the line segments make a 90° angle then they will be perpendicular. But the line segments may not be 90°.

Answer 6

fake in case you %. a level, draw a ray from it then draw yet another ray from it in the different direction ... are they perpendicular? (perpendicular signifies that they intersect and both angles upload as a lot as be ninety ranges (both accurate angles)

Answer 7

true when the angle contained is 90 degrees.it need not always be 90 degrees.therefore the statement is not true always