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  • Write whether the following statements are True or False? Justify your answer: Two distinct intersecting lines cannot be parallel to the same line.

Write whether the following statements are True or False? Justify your answer: Two distinct intersecting lines cannot be parallel to the same line.

Answers (1)

True

Solution:

Euclid’s fifth postulate: if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.

Using the above, we can see that two distinct intersecting lines cannot be parallel to the same line.

Here we can take an example: line AB and CD are intersecting. If we take a line EF parallel to AB then EF is not parallel to CD.

Hence the given statements is true.

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