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Two lines parallel to the same plane are parallel to each other?
they are transversals to each others
Where do two distinct parallel lines intersect?
A vertex? In non-euclidean geometry: A two distinct parallel lines intersect in the "Infinity zone"
What patterns do you observe among the angle measures?
There are different patterns in different circumstances: for example when two (or more) parallel lines are intersected by one (or more) transversals; or when considering the interior or exterior angles of polygons.
What pairs of distinct lines or line segments of a circle cannot be parallel?
Pair of radii
What does it mean when the angles are on the same side?
Usually this is about parallel lins and transversals. Imagine 2 horizontal lines which are parallel. Now imagine a transverse line from uper left to lower right crossing thru the two parallel lines. This makes 8 angles. The top line and the transversal create an angle on the upper right. So does the lower line and the transversal. These are on the same side of the transrevsal.
Two lines parallel to the same plane are parallel to each other?
they are transversals to each others
Can transversals be parallel to each other?
Sure. You could have a set of parallel lines crossed by two transversals that are parallel to each other. The figure formed by their intersection would be a parallelogram! That's one way of looking at it...
Lines m and n are parallel if lines m and n are cut by three different transversals which also what is the least number of points of intersection that can occur among five lines?
four
Where do two distinct parallel lines intersect?
A vertex? In non-euclidean geometry: A two distinct parallel lines intersect in the "Infinity zone"
Two distinct lines that do not intersect are parallel?
2 lines the same width apart are parallel.
If two distinct lines intersect?
Then they are not parallel, nor skew (in 3D).
What patterns do you observe among the angle measures?
There are different patterns in different circumstances: for example when two (or more) parallel lines are intersected by one (or more) transversals; or when considering the interior or exterior angles of polygons.
What pairs of distinct lines or line segments of a circle cannot be parallel?
Pair of radii
What does it mean when the angles are on the same side?
Usually this is about parallel lins and transversals. Imagine 2 horizontal lines which are parallel. Now imagine a transverse line from uper left to lower right crossing thru the two parallel lines. This makes 8 angles. The top line and the transversal create an angle on the upper right. So does the lower line and the transversal. These are on the same side of the transrevsal.
How many points does 5 intersecting lines have?
If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 10 points of intersection.
How many points do 4 intersecting lines have?
If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 6 points of intersection.
How many points does 1000 intersecting lines have?
If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 499500 points of intersection.
