Thread: Parallel line contruction

Hi! I am Utsav again.

Please tell me again in detail that how can I draw a line parallel to any side of a triangle

without measuring any angle.

And please also tell me if there is any property or proof for the solution of above problem.


Utsav

extend two of the lines equal distances (the extension is marked as two red lines), because the lines stay at the same angle, than the line created connecting the two has the same angles as the original line (the blue lines are parallel).

Originally Posted by utsavfromfuture

Hi! I am Utsav again.

Please tell me again in detail that how can I draw a line parallel to any side of a triangle

without measuring any angle.

And please also tell me if there is any property or proof for the solution of above problem.


Utsav

How do you mean? Usually you wish to draw through a point a line parallel to the given line. Which is that point here? (The vertex?)

Originally Posted by Quick

extend two of the lines equal distances (the extension is marked as two red lines), because the lines stay at the same angle, than the line created connecting the two has the same angles as the original line (the blue lines are parallel).

I think that if you will extend two lines by the same distance, then the resulting new line may or may not be the line parallel.
We are extending two sides, Let AB and AC. Extend AB by the distance equal to AB. Extend AC by the distance equal to AC. Now you will definitely get parallel line.

Keep Smiling
Malay

Originally Posted by malaygoel

I think that if you will extend two lines by the same distance, then the resulting new line may or may not be the line parallel.
We are extending two sides, Let AB and AC. Extend AB by the distance equal to AB. Extend AC by the distance equal to AC. Now you will definitely get parallel line.

Keep Smiling
Malay

Too true, because this would form a similar triangle with a ratio of 2:1 compared to the beginning one. (thanx for pointing that out)