Question

Please solve..........

If a line 'l' is not parallel to 'm' and given that 't' intersects 'l' then prove that 't' also intersect 'm'.

Answer 1

Here we have two non parallel lines l and m , And a line t intersect l .

As we know from Euclid's fifth Postulate: That, 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 of which are the angles less than the two right angles.

And given l and m are not parallel lines so at some point they also intersect each other ,

And if we have third line that intersect first line also intersect second line at some point whether these line l and m are parallel or not , As we have transversal line that intersect two or more parallel line and also two or more non parallel lines .

So if we have third line t that intersect line l that also intersect line m at some point .

Answer 2

Answer:

If a line 'l' is not parallel to 'm' and given that 't' intersects 'l' then 't' also intersect 'm'.

Step-by-step explanation:

Intersecting lines: When two lines in a plane cross each other with only one common point between them are called intersecting lines and the point is called the point of intersection.

Parallel lines: When two lines in a plane when extended endlessly to infinity do not cross each other are called parallel lines.

Given three lines l, m, t and relations between them.

• l is not parallel to m, so l and m intersects at some point.

l and m are intersecting lines.

• t intersects l, so t and l are intersecting lines.

If l,

Two intersecting lines can never be parallel to the same line.

So l and m are intersecting lines, so they can never be parallel to t.

So t also intersects m.

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