Supplementary Angles That Do Not Form A Linear Pair

Supplementary angles that are not a linear pair are found all over our world. They are found most commonly found as two right angles. Within a box like figure, there are right angles in the corners. Two right angles will always form a pair of supplementary angles. Based on the definition of a right angle, there is 90 degrees in the angle. This means two right angles add up to 180 degrees. By definition, this means two right angles from a pair of supplementary angles. On example of supplementary angles that are not a linear pair are the angles within a lacrosse goal. These two angles are automatically a pair of supplementary angles because they are both right angles. Also, the are not a linear pair for they are non-adjacent. This is my lacrosse goal but this same geometric concept can be found in plenty of other areas of the world. The corners of a building, the corners of a chalkboard, and the corners of a TV are all other good examples of supplementary angles that do not form a linear pair. 

Non Congruent Alternate Interior Angles

Non congruent alternate interior angles occur when two non parallel lines are intersected by a transversal. In the diagram above, the two legs of the chair act as the non parallel lines while the seat acts as the transversal. If the two legs were parallel, then the alternate interior angles would be congruent. In the real world, congruent alternate interior angles are much more common. Things in the real world, such as a buildings, are normally created with parallel and perpendicular lines because they are more sturdy.  

Skew Lines

Skew lines in a math dictionary are defined as,  two lines in space that do not intersect and are not parallel. For this to be true, the two lines must be on different planes and traveling different directions. In the real world, skew lines are seen all over the place. Skew lines are practically in every 3 dimensional figure. Buildings, chairs, and even goal posts (as shown above) contain skew lines. Skew lines are a very basic geometric idea in architecture that lead to the creation of many different figures. Because of this, skew lines have a very great impact on our modern world.