Non-congruent alternate interior angles

This picture shows non-congruent alternate interior angles. The purple angles show two interior angles. The angles aren't congruent because the do not have the same length. They are alternate because they are on opposite sides of the transversal. They are interior because they are on the insides of the transversal. I took this picture myself with pencils I found in my house. Pencils are an everyday object that students, teachers, doctors, etc. use as a writing utensil.  

Segment bisector

A segment bisector is a line that intersects a segment at the midpoint. In the image above, the green line passes through the blue segment at the midpoint. This picture was taken on my phone using ribbon. Ribbon is a strip of fabric used to tie something or for decoration. Anyone can use ribon for decorating or tying up their hair.

Skew lines

Skew lines are two lines that do not intersect, but they are not parallel. In the image above, the two lines (chopsticks) are not parallel and will never intersect, making them skew lines. Skew lines are always in different planes. This picture was taken on my phone of a pair of chopsticks I found in my room. Chopsticks are used to eat with and pick up food and are mainly from China.

Adjacent non-supplementary angles

This picture shows an adjacent non-supplementary angle. The angles share a vertex and a common side, the white line. The angle is not supplementary because their measures do not add up to 180 degrees. This photo was taken on my phone of socks making an adjacent non-supplementary angle. Socks are a clothing article that people put on their feet to keep them warm. The socks were found in my room.

Supplementary angles that are not a linear pair

This picture shows supplementary angles (in green) that are not a linear pair. A linear pair is formed when two lines intersect. These lines do not intersect and are not adjacent, therefore not a linear pair. They are still supplementary, though, because their sum is 180 degrees. This picture was taken with my camera. The angles are formed from a bird's eye view of birthday cards. Birthday cards are used for people to wish a happy birthday to their friends or family. These cards were found in my room.

Vertical angles

The legs of the piano stand intersect and form two pairs of vertical angles. Vertical angles are formed when two lines intersect. Each opposite pair are called vertical angles and they are congruent. The single red curved lines show a set of vertical angles and the double yellow curved lines show another set of vertical angles. When collapsing the keyboard stand, the angles stay congruent because vertical angles always stay congruent no matter the height. I took this photo of the keyboard in my basement and the legs are used to hold up a piano. Piano falls under the category of music industry.

Angle bisector

This picture of noodles forms an angle with an angle bisector. The purple lines show the acute angle and the green line shows the angle bisector. The middle noodle is an angle bisector because it divides the space between the other two noodles or the angle into two equal parts. The noodles can be found at a grocery store of any kind but I just used ones within my house. They are used for eating. I took this picutre myself and noodles fall under the category of food.

Congruent acute or obtuse angles

Angles are congruent if they have the same angle measure in degrees. These scissors contain congruent acute angles (drawn on in purple). They are acute because they both have measurements less than 90 degrees. The angle at which the scissors open both have the same dimensions and shape, making them congruent. Scissors are a househeld object and are used to cut things. I took this photo myself and scissors are part of the metal fabrication industry.  

Line perpendicular to a plane

A line is perpendicular to a plane if and only if the line intersects the plane in a point and is perpendicular to every line in the plane that intersects it at that point. This picture shows a pencil intersecting an advertisement. The red line (pencil) intersects the blue plane (the advertisement) because it goes through the plane and is a right angle to another line in that plane. The ad was found in a magazine and the pencil was found in my backpack. The ad relates to the real world because it is how companies broadcast their ideas to the general public. I took this picture on my own camera. This picture portrays the marketing industry because of the pencil intersecting the advertisement.

Three or more coplanar parallel lines

Coplanar lines are lines lying in the same plane. This keyboard contains multiple coplanar parallel lines (in red). The lines in between the keys are straight, will never intersect, and are in the same plane. The keyboard was found on my laptop, and is used everyday by many because it is what helps you type on a laptop. Keyboards can be used by authors, students, teachers, etc. A keyboard falls under the category of information technology because many researchers use the technology of laptops and find data. I took this photo on my camera.