Non-congruent alternate interior angles

Pictured here are three contrails intersecting that create non-congruent alternate interior angles. The two thicker contrails on the outside are cut by a transversal contrail, and this always makes interior angles, but since the two outer lines are not parallel I also know that the interior angles are not congruent. Contrails are created from the exhaust from jets and planes cutting through the air. Ever since planes started becoming more commercial about half a century ago, contrails have been seen all over the sky. On a clear, blue-skied day, contrails can always be seen above dicing up the clean blue sky. Contrails are not so much used as they are just seen and noticed on an everyday basis. In my life I dont believe I have ever seen a perfectly blue sky without contrails cutting through it. Contrails are created by thousands of pilots everyday and seen by millions and probably billions of people on the ground everyday.

I found this image online at this address: http://astrobob.areavoices.com/tag/contrail/

Segment bisector

Pictured here is a cross, one of the most recognizable objects in the world. The vertical part of the cross intersects with the midpoint of the horizontal part of the cross. The vertical part is therefore a segment bisector because it intersects with midpoint of the horizontal segment, creating two equal pieces on each side. The cross became famous way back in 32 A.D. when Jesus was put on one. Since then it has became the symbol of the biggest religion in human history. They are seen as a holy symbol by Christians and can be found on Bibles, churches, and at every Christian institution. Crosses are often prayed to and gone to when seeking spiritual guidance. A few people that can be seen with a cross are Pope Francis (great guy), followers of Christianity across the world, and famous figures throughout history.

I found this image online at this address: http://www.holidayatthesea.com/?p=6031

Skew lines

Pictured here is the Golden Gate Bridge going over the entrance to San Francisco Bay. The line down the center of the channel and the bridge itself form skew lines. Skew lines are non-parallel lines that are not in the same plane. The bridge is above the water so that separates the planes and they are going in opposite directions so are clearly not parallel. The Golden Gate Bridge is arguably the most famous bridge in the world. The two mile bridge was built in 1937 and since then has become one of the most recognizable symbols of not only San Francisco but also the entire United States. The bridge is used by millions of people every year and is a sight to behold. Yet it's also very practical because before it was built, the fastest way to get across the bay was by ferry. The bridge has lots of both foot and car traffic and nearly every person in America has seen an image, usually from the same spot taken here, in their life.

I found this image online at this address: http://www.nevworldwonders.com/2013/09/preview-golden-gate-bridge.html

Supplementary angles that are not in a linear pair

Pictured here is an iPad keyboard. The right angles formed by the keys are supplementary to each other. I know this because the measure of right angles are 90 degrees and for two angles to be supplementary their sum must be 180 degrees. Keyboards have turned into a common product since the invention of the computer and can be seen on an every day basis at school. They are used for typing on your electronic device and are very useful and efficient for taking notes and writing papers. People that can be seen with a keyboard include Bill Gates, Ms. Fort, and Mr. Lagarde. I found this object in my backpack and use it nearly everyday. 

  

Adjacent non-supplementary angles

Pictured here is a common green leaf. The two 'veins' of the leaf come from the stem to form two adjacent non-supplementary angles. They are adjacent because they share a side yet are clearly not supplementary, meaning their two angle measures add up to 180 degrees. Leaves can be seen all around us everywhere and everyday. Now, in the winter, there are much less due to the cold climate but in a few months green leaves like this will be budding everywhere. Leaves are not only beautiful but also essential to human life. They create and filter oxygen which we breathe at all times. Leaves are amazing things and have been seen by nearly everyone on the planet. Leaves can come in countless shapes, sizes, and colors. 

I found this image online at this address: http://en.wikipedia.org/wiki/Leaf

Vertical angles

Pictured here is a small-sized football I own at my house. The seams of the football intersect to form four angles which are vertical angles. Vertical angles are angles that are opposite from each other and also congruent. In this case, because the seams are perpendicular to each other, the four angles are all right angles as well. Football is currently the biggest and most popular sport in the United States by far. A football is essential for playing the sport and is a simple yet very entertaining object. Many people can be seen with a football, including Peyton Manning, Tom Brady, and Joe Flacco. I found this object with other sports items in my house. 

Angle bisector

Pictured here is clock that is at approximately 3:05 and 25 seconds. The hour hand acts as an angle bisector between the angle formed by the minute and second hands. I know it bisects this angle, forming two congruent angles, because there is exactly ten minutes between the hour hand and both the minute and second hands. Clocks like the one pictured have been around since about the 12th century and have been an amazingly useful invention ever since. Knowing the time of day is something we take for granted with our phones now but it's something we just always need to know and it constantly effects our lives. I believe that nearly every person in the world has seen a clock at some point in their lives. Clocks can be found on watches, iPhones, and simply clocks on the wall. 

I found this image online at this address: https://sites.google.com/site/mymathclassroom/trigonometry/clock-angle-problems/clock-angle-problems-involving-second-hands

Congruent obtuse angles

Pictured here is the top portion of a lacrosse stick. The straight pole of the stick and diagonal lines of the head form two congruent obtuse angles. The angles are congruent because they are adjacent and the diagonal lines of the head leave the pole at the same angle and they are obtuse because they are visibly larger than a right angle but not quite a straight angle.  Lacrosse is the fastest growing sport in the U.S. and can be found across the country and a lacrosse stick is always needed to play. It is used to scoop up ground balls, to pass, and to shoot. Many people can be found with a lacrosse stick, including Tyler and I and other athletes across the country. 

I found this photo online at this address, http://365sportsonline.com/en/sticks/20022965-stx-stinger-jr-lacrosse-stick.html

Line perpendicular to a plane

Pictured here is the chain of a chandelier which is perpendicular to the ceiling. The chain of the chandelier isn't a true line because there are no lines that go on forever in real life. Yet it is a segment that goes until it hits the roof where it makes a right angle which means it is perpendicular. The flat surface of the roof represents the plane that the segment is perpendicular to. I took this photo upstairs at my house and chandeliers can be found in many houses. It is an object used because of its design and beauty but also for its effect which is illuminating areas. Many American families may have a chandelier but they can be found in homes across the world. 

Three or more coplanar parallel lines

This is the Beatles' Abbey Road album cover. This is one of the best selling and critically acclaimed albums in music history, and has one of the most famous album covers ever.The four members of the Beatles, John Lennon, Ringo Starr, Paul McCartney, and George Harrison are all pictured walking in a single-file line. The red and green lines represent the parallel lines formed by each member's back. And these lines are in the same plane because all parallel lines are always in the same plane. I found this picture on the internet and the album has been seen, used, and heard by hundreds of millions of people. To listen to music in the 60's and 70's, people had to buy records and these records had covers, so being a best-selling album countless people have seen this album cover. These people may include, but are not limited to, classic rock music fans, the Queen of England, and various musicians. 

I found this image online at this address: http://www.vinylrecords.ch/B/BE/Beatles/Abbey_Road/abbey_road.htm