Describe postulate no.5 with a illustration.
Q2. EUCLID'S FIVE POSTULATES
POSTULATE 1. A straight line may be drawn from one point to any other point. Given two distinct points, there is a unique line that passes through them.
POSTULATE 2. A terminated line can be produced indefinitely.
POSTULATE 3. A circle can be drawn with any centre and any radius.
POSTULATE 4. All right angles are equal to one another.
POSTULATE 5. For every line L and for every point P not lying on L, there exists a unique line M passing through p and parallel to L.
Dear student
The Euclid's 5th postulate states that "For every line L and for every point P not lying on L, there exists a unique line M passing through P and parallel to L."
i.e.
This can also be rewritten in simple words as:
Two distinct intersecting lines cannot be parallel to the same line.
This means Euclid’s fifth postulate imply the existence of parallel lines.
Illustration:
If a straight line ‘l’ falls on two lines ‘m’ and ‘n’ such that sum of the interior angles on one side of l is two right angles, then by Euclid’s fifth postulate, the lines will not meet on this side of l. Also we know that the sum of the interior angles on the other side of the line l will be two right angles too. Thus, they will not meet on the other side also.
Regards
The Euclid's 5th postulate states that "For every line L and for every point P not lying on L, there exists a unique line M passing through P and parallel to L."
i.e.
This can also be rewritten in simple words as:
Two distinct intersecting lines cannot be parallel to the same line.
This means Euclid’s fifth postulate imply the existence of parallel lines.
Illustration:
If a straight line ‘l’ falls on two lines ‘m’ and ‘n’ such that sum of the interior angles on one side of l is two right angles, then by Euclid’s fifth postulate, the lines will not meet on this side of l. Also we know that the sum of the interior angles on the other side of the line l will be two right angles too. Thus, they will not meet on the other side also.
Regards