Composite Solid

      This is a goldfish box that I saw while shopping at the grocery store. Instead of being the pre-packaged goldfish, it is goldfish in a small milk cartoon like contanier. This is a composite solid because the base of the box is a rectangular prism and top where you open the box is a triangular prism. The shape of this box is certainly not a coincidence. The goldfish company must have been looking for a new way to present their food other than in baggies. The rectangular prism is the crucial part of the structure that holds the goldfish. The triangular prism is there as a way of opening the box. This opening style is similar to a milk cartoon. One has to peel two of the faces back to get it open. Since this item was near the checkout at the grocery store, they acted as a nice "to-go"snack because they are easy to grab and go. The prepackaged bags, on the other hand, are not a composite solid so they are not easy to hold and all of the goldfish are less likely to stay in the bag. 

A Regular Polygon With More Than 5 Sides

     This is a picture of a pre-cut vegetable container from the grocery store. Obviously the veggies were already eaten, but they were once held in the shape of a regular octagon. A regular polygon means that all sides and angles of the shape are congruent. This vegetable container is a regular octagon because each of the eight sides are the exact same length. Part of the reason for it being constructed this way is for the look. A neat, congruent-sided shape unconsciously appeals much more to the buyer than a blob-shaped container with some carrots in it. This applies to the same logic of a stop sign. Now everyone knows the classic shape of a stop sign is a regular octagon, and they like it that way. If the word stop was printed on a curved and lopsided sign, everyone would think about the unsophistication of that town or city. Also, a regular-shaped vegetable container usually uses the congruent sides as way to divide each veggie. If the place where the ranch was supposed to go acted as the center, then there would be 45 degrees for each veggie. Using a circle concept to divide 360 degrees by 8 sides, the container will have a much more organized look, which will get it purchased faster. 

Supplementary Angles That Are Not A Linear Pair

     My grandparents' house has a small roof over the front porch. The two parallel lines are formed by one side of the main house and another side of the jutting out part. The line along the porch roof is a transversal to those two parallel lines. Because of consecutive interior angles, we know that angle one and angle two are nonadjacent supplementary angles. Architecturally, the two parallel lines are parallel because they have to both be perpendicular to the ground in order for the house to stand. The line along the small roof has to protect the porch and let water drip from it, thus allowing it to be slanted and not perpendicular to the parallel lines. Many objects in the real world have two parallel lines cut by a transversal, such as window frames, but those have 90 degree angles. My picture/example of nonadjacent supplementary angles is unique, as angles one and two are not congruent.     

Non-congruent Alternate Interior Angles

      This is the railing beside the stairs on the outside of my grandparents’ house that has many vertical poles, one diagonal pole, and horizontal poles holding everything together. The vertical pole acts as the transversal to the diagonal and horizontal poles. And because these two poles are not parallel, the alternate interior angles are not congruent. Many houses have a railing leading up to their front door, so the horizontal and vertical poles (that are perpendicular) provide support for it to stand up straight. But, the diagonal pole, in the picture below, acts as a hand rail and extra support for the railing itself. Almost any building or house in the world that has stairs, uses a railing for support and safety reasons. It is especially helpful that the diagonal pole and the horizontal pole do not provide alternate interior angles because people need a stronger support system to grab when walking up stairs or an incline. And non-parallel lines give a structure something diferent and sometimes stronger to work with. 

Skew Lines

          These are my mom’s reading glasses and they contain many pairs of skew lines. It has two frames, for the eyes to see through, and then two thin “poles” that hold the glasses on her ears. The vertical line of the frame is in a different plane and never intersects with the thin “pole” that goes behind the ear. After my mom set her glasses down, I saw the pairs of skew lines such as a vertical frame line to a “pole” line, and the same thing on the other side. This specific way that the shape of glasses are made provides the most comfort and functionality of whoever is wearing them. Therefore, if the glasses only had horizontal lines, there would be no skew lines, and no way to possibly wear those glasses. The structure of glasses has worked for many years and will continue to work, even as we reach new inventions such as the HoloLens. 

Congruent Isosceles Triangles

      My waffle maker has four sections that create “waffle triangles” and is used on holidays or special occasions. Even though one edge of each triangle is slightly rounded, the finished products are almost perfectly straight. All four triangle sections are congruent to each other, and the sides that they share are also congruent. Because they both have two congruent sides, they also have two congruent angles. When my family had the waffle maker sitting out on the kitchen counter, I quickly noticed the congruence of the shapes that form the waffle. Waffle makers are very common in households as well as restaurants. We use the waffle maker for Christmas Brunch and it is used by others at diners, breakfast shops, and other places. Also, the congruent triangle set-up makes the waffles prettier to serve and easier to eat, as the triangles are very similar to a slice of pizza.