Composite Solids

This my Canon Eos 7D. Cameras are used all over the world to capture images. This camera is a composite solid. It is made up of two geometric shapes. The camera body makes up a rectangular prism and the lens makes up a cylinder. These two shapes connect to form a composite solid. There are many other examples of this in the real world as well. Every house is just a collection of geometric shapes. Each room makes up a rectangular prism and the roof makes a pyramid.  

Regular Hexagon

The object shown above is a table. This table's surface is a regular hexagon. It is a regular polygon because it's a closed figure, has straight lines, and all sides and angles are congruent. I found this table in my living room. Shapes like this are seen all over the world in stop signs as well. All of the sides and angles are congruent withing a stop sign. In nature, we see regular hexagons made by bees. As bees make their honey, the honey comb forms regular hexagons. Regular polygons are seen all over and are shown in the shapes of the world. 

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. 

Congruent Isosceles Triangles

If two triangles are are congruent to one another and they are both isosceles, then they will have equivalent side lengths and congruent base angles. Slices of pizza are a prime example of congruent isosceles triangles. In the diagram above, the two missing slices were congruent by the AAA Theorem.  

The two base sides are tangent to the circle. They are also opposite each other causing them to be parallel. The two pairs of base angles are congruent based upon the alternate interior angles theorem. The two non-base angles are congruent based upon the vertical angles congruence theorem. Based of these geometric ideas, slices of pizza are congruent triangles. By definition, isosceles triangles have two congruent sides. In this case, the pizza was cut into isosceles triangles, however it could have been cut into equilateral triangles (these are still isosceles). In the real world, when people order a pizza, they want it cut so that each will get the same amount. By cutting a pizza into congruent triangles, this is assured.