Non-Congruent Alternate Interior Angles

Waffle Cone

This waffle cone has an example of non-congruent alternate interior angles. The sides of a waffle cone (pink) are not parallel which makes the alternate interior angles  cut by a transversal (blue) not congruent. For example, angle one and two are non-congruent alternate interior angles, because the two biggest exterior lines are not parallel. Waffle cones can be found in the local ice cream parlor shop, restaurants, or at the grocery store. Kids, adults, ice cream scoopers, and ice cream lovers use waffle cones to eat their ice cream.

This picture was found online: http://www.capitalcateringsupplies.co.uk/BS%20GF%20Twist2.jpg

Segment Bisector

Window Frames

This window frame, used in this example as a frame on a cabinet, uses the lines in structure to show a segment bisector. The vertical part of the frame (blue line) is a segment bisector because it cuts the horizontal side of the frame (green line) into two equal segments. The green line intersects the segment at the midpoint which makes it a segment bisector.  Window frames can be found in all types on buildings, but are most popular in houses. They add style to a basic window. Construction workers, kitchen installers, and dads that are good with tools can be found using this object.

This is a picture taken by me.  This cabinet can be found in my kitchen.

Skew Lines

Diving Board

This diving boards represents skew lines with the side of the board (orange)  and base (green). Skew lines are lines that are not parallel and will never intersect. The side of the board and the base of the diving board are skew lines because  they follow the rules of the definition. The orange and green lines on the diving board are not parallel and will never intersect. Diving boards can be found in a backyard, at a neighborhood swim club, aquatics center, and the Olympics for recreational fun or for the competitive sport. Kids, adults, and divers use this apparatus for jumping, flipping, or belly flopping into a pool.

This picture was found online: http://www.malmsten.com/img/huvudbilder/13400_1_S.jpg

Supplementary Angles that are not a Linear Pair

Cross Necklace

This cross necklace shows supplementary angles that do not form a linear pair because the angles are not adjacent. Both angles are right angles. All right angles are 90 degrees, making them supplementary. The two angles are also congruent because of the definition of right angles. Cross necklaces are a symbol for certain religious beliefs. Men, women, boys, and girls who are followers of Christian religion are known to wear these necklaces.

This necklace was found online:http://www.houseofharlow1960.com/Images/ProductFull/37858-135/cross-pendant-necklace.jpg

Adjacent Non-Supplementary Angles

Sailboat

The sails on a sailboat are an example of adjacent, non-supplementary angles because they share a common side (brown).  The two angles are also non-supplementary because the sum of the measures of both angles does not equal 180. Sails catch wind causing the sailboat to move. These are essential items to a their main users, sailors, to navigate and operate the boat.

This object was found online:  http://img.nauticexpo.com/images_ne/photo-g/sailboats-cruising-sailing-yachts-ketch-20644-205537.jpg

Vertical Angles

Salad Tongs

These salad tongs have two pairs of congruent vertical angles. Angle one and angle 4 form a linear pair, and so do the two opposite angles, angles two and four. The angle closest to the handles of the tongs (angle one) and the angle closest to the mouth of the tongs (angle three) are congruent by the definition of vertical angles. Salad tongs are used in restaurants, homes, barbecues, and buffets. Anyone from a chef to a house mom uses this type of tongs to serve salad/food.

This photo was taken by me. These salad tongs can be found at my house.

Angle Bisector

Office Chair

An angle bisector is shown through the legs of the chair. The yellow leg cuts the blue angle (made up of other chair legs) into two smaller equal angles. An angle Bisector is a line or line segment that cuts an angle into two equal parts. Therefore, the yellow line is the angle bisector in this situation which cuts the angle made by the blue legs into two equal parts. Office chairs can be found at work places, homes, or Ms. Fort's classroom. Many professionals use these chairs every day in their offices, work places, or classroom.

This picture was found online: http://www.1stseniorcare.com/images/ERA-bariatric/ERA-Malibu-Bariatric-office-chair-BigChair-Huge.jpg

Congruent Obtuse Angles

Pool Chairs 

These pool chairs show an example of congruent obtuse angles. The backrest and side of the chair form an obtuse angle. The back rest of both chairs are placed at the same angle (level) making both chair angles congruent. The angles made by the parts of the chair are greater than 90 degrees (a right angle) and less than 180 degrees (a straight angle/line) making them obtuse angles. These chairs can be found in a backyard, at a community pool, or maybe even at the beach. Adults, kids, or anyone trying to get a nice tan uses these chairs during the hot summer months.

This picture was found online: http://media-cdn.tripadvisor.com/media/photo-s/02/8d/c5/08/filename-chairs1-jpg.jpg

Line Perpendicular to a Plane

Field Hockey Goal

This field hockey goal has a line that is perpendicular to a plane. The backboard of the goal (yellow plane) is perpendicular to the side board of the goal (pink line) because when the two parts of the goal meet/intersect, they form a right angle. The definition of parallel lines (planes contain lines) is that when two lines intersect, they form a right angle. The structure of the goal, with the backboard as a plane and side board as a perpendicular line, follows the definition of parallel lines. These goals can be found all around the world at either field hockey fields or courts.  Field hockey players, toddlers to adults, use these goals to practice their shots and to score in games.

This picture was found online: http://www.networldaustralia.com/media/catalog/product/cache/1/image/9df78eab33525d08d6e5fb8d27136e95/f/i/file_28_7.jpg

Three Coplanar Parallel Lines

Kitchen Island 

This side of a kitchen island contains multiple parallel lines that are coplanar because they are all on the same plane and do not intersect. The lines are highlighted in orange, yellow, pink, and grey. All of the highlighted lines have the same slope which makes them parallel. This type of siding can be found in kitchens, and similar siding can be found on walls and the exterior of houses, and it used for structure and style. Many construction and kitchen appliance workers use this material when building or renovating a house.

These pictures were taken by me.  This island can be found in the kitchen at my house.