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If two parallel lines are cut by a transversal then the alternate interior angles are always?
Congruent
If two parallel lines are cut by a transversal then are the alternate interior angles always supplementary?
yes because they will always equal 180 degrees, regardless of the angle at which the transversal intersects the two parallel lines
What is a pair of angles that lie between the parallel lines on opposite sides of the transversal?
Those are "alternate interior" angles. They're always equal.
What is the word for this definition Angles that are inside parallel lines that are cut by a transversal?
Alternate and interior angles are created between parallel lines when a transversal line cuts through them.
Alternate interior angles?
They are always equal on the transversal line that cuts through parallel lines
Which angle pairs are always congruent if a transversal cuts two parallel lines?
The corresponding and alternate angles
Would two lines be parallel if the consecutive interior angles measured 108 degrees and 74 degrees Explain?
No, two lines would not be parallel if the consecutive interior angles measured 108 degrees and 74 degrees. Consecutive interior angles on parallel lines are always congruent, meaning they have the same measure. Therefore, if the consecutive interior angles have different measures, the lines cannot be parallel.
What is always true about rectangules?
Rectangles are always 4 sided quadrilaterals having 4 interior right angles of 90 degrees and two pairs of opposite parallel lines of different lengths
Is the 'claim' always the alternate hypothesis?
No.
Is a trapezoid a 360º figure?
Yes the 4 interior angles of a trapezoid add up to 360 degrees
Does a trapezoid always have 2 parallel sides?
Yes - it always has exactly two parallel sides.
Parallel lines are equidistant and will never meet?
I understand your question to be, "Is it true that parallel lines are everywhere equidistant and never intersect?" In what follows, I assume we're talking about a two-dimensional plane. By definition, two lines that are parallel (in the same plane) never intersect. In Euclidean (AKA Parabolic or simply E) Geometry, and also in Hyperbolic (AKA simply L) Geometry, parallel lines exist. In Elliptical (AKA R) Geometry, all lines eventually intersect so parallel lines do not exist. Now, are two parallel lines (in the same plane) everywhere equidistant? If so, that means that it is possible, at any point on one of the lines, to construct a perpendicular that will meet the other line in a perpendicular, and that the length of the segments constructed will be always the same. In Euclidean Geometry, two parallel lines (in a plane) are indeed everywhere equidistant. To prove it requires the converse of the Alternate Interior Angles theorem (AIA), which says that if two parallel lines are cut by a transversal, the alternate interior angles will be congruent. Note that this is the CONVERSE of AIA, not AIA. Some people get this mixed up. In Hyperbolic Geometry, two lines can be parallel, but be further apart some places than others. I know that sounds rather odd, if you're not used to it. Here's an image that might help: imagine that your plane is a thin sheet of rubber, and for some reason is being stretched. The further you go from your starting point, the more it stretches, and it's always stretching away from you. This means that your parallel lines will keep getting further and further apart.
