Non-congruent Alternate-Interior Angles

This image is of the letter A. This is an extremely important letter, being one of 6 vowels. The letter A is used the the English alphabet, and is used in a high percentage of words. The letter A also exhibits the property of non-congruent alternate-interior angles, because this letter has two main lines cut be a transversal. However, the main lines intersect, and so are not parallel, which means that the alternate interior angles are not congruent. This image was found using google images, under the URL http://www.wickes.co.uk/self-adhesive-cut-out-letter-a/invt/191091/. 

Skew Lines

This photo is of a fence. Fences are used very commonly today, to mark property lines and separate crops. Fences are sometimes used as barriers, as seen in jails. However, fences demonstrates skew lines, because the vertical post does not intersect with the horizontal posts. The two different directions of posts are in two different planes, and are not parallel. This particular image was found at http://www.lowes.com/cd_Fence+Buying+Guide_976084218_, through google images. 

Adjacent non-supplementary angles

This is an arrow. Arrows are used today for many reasons. Arrows are used on signs to point which way to turn. Arrows are used on maps to point out specific locations. Arrows pointing to something are used to emphasize it. But, arrows also show adjacent non-supplementary angles, because they have two angles that share a side and a vertex, and because an arrow needs to point to something, the head does not form a flat line, because then it would not indicate a direction. This particular image was found through google images, using the URL http://www.designofsignage.com/application/symbol/hospital/largesymbols/arrow-down.html. 

Segment bisector

This picture is of a Christian Cross. The cross is used to symbolize the religion, and is often featured as an item of decoration within the Church. The cross also forms a segment bisector, because the long section of the cross bisects the shorter section. This particular image was found using google images, under the URL http://johnvoelzblog.blogspot.com/2012/01/no-cross-at-church.html. 

Vertical angles

This is a picture of a treasure map, found through google images at the URL http://tex.stackexchange.com/questions/86804/pirate-treasure-map. A treasure map is a map made by pirates so that ye can always know the location of their buried treasure. However, the "X" in a treasure map also forms a pair of vertical angles, because an x is formed of two lines, and where the lines intersect, two pairs of vertical angles are formed. Treasure maps are useful tools to give children an adventure, and are often seen in TV shows, books, and comics.

Congruent obtuse angles

This is a sword display rack. The swords are arranged in an x shape, so they form a pair of obtuse vertical angles. This object was found in the URL http://www.usmilitaryswordsonline.com/Walnut-Large-Sword-Display-Shield_p_12.html through google images, and is often used to decorate houses, castles, museums, and other places where people spend time. 

Angle bisector

This object was a very useful one. It was called an Egyptian plumb line, and was used to determine of a surface was level or not. Plumb lines were used in the construction of the pyramids, and can still be used today. A plumb line  is an angle bisector when a surface is completely level, because the string hangs right in the middle of the angle formed by the stands. I myself built a version of this kind of level, where a string hangs down with a weight on it. This picture was found at the URL http://www.touregypt.net/featurestories/tomb.htm, through google images. 

Line perpendicular to a plane

This object is a flagpole. It is a pole that sticks strait up out of the ground, and is used to hang a flag as a symbol of a country. Flagpoles are also used to send distress signals, such as hanging a US flag upside-down. This object represents a line perpendicular to a plane because the pole itself sticks right up,our of the ground at a right angle, so the pole is perpendicular to the ground. This photo was also 

found on google images, in the URL http://www.gettysburgflag.com/index-Poles.php.

Supplementary angles. Not a linear pair

This object is a carpenter's square, a very useful tool. It shows a pair of supplementary angles that are not a linear pair, because of its perfectly right properties. The carpemter's level is used to measure if a corner forms a right angle, and so, there is more than one right angle inside it. This picture was obtained from the URL http://www.daviddarling.info/encyclopedia/C/AE_carpenters_square.html, using google images. 

Parallel lines

This picture is of three coplanar parallel lines. It is found in one of the Nazca drawings, on the Nazca Plain. This picture was obtained from google images, under the URL http://www.bbxrafting.com/nazca-lines. This object shows parallel lines in the bird's tail, where the lines that make the feathers have the same slope, do not intersect, and are in the same plane. In the real world, this picture is visited by tourists every month, because it was made hundreds of years ago,and it is a great mystery how the natives did it without planes or a way to monitor their work from the air.