Geometry in an Old Sailing Ship

This picture shows an example of perpendicular lines in the ship's sail and mast. There are also examples of an isosceles triangle in the ropes on top. In the middle, there is a crows nest that shows an example of a circle, with the mast going through its center. (~CD1)

Proving Theorem 9-5 with a Car Tire

As theorem 9-5 states, "a diameter that is perpendicular to a chord bisects the chord and its arc." I decided to use a picture of my car tire to show the proof of this theorem. 

~ (JC2)

Books

This is a picture of a bunch of different symbols from books put together (Percy Jackson, Harry Potter, The Mortal Instruments, The Hunger Games, Divergent).

In this picture, there are three circles. The center one is externally tangent to both of the circles on either side of it. The vertical line in the middle of the picture is also the diameter of the center circle.

This image also has two lines that are externally tangent to the center circle (lines j and k). The right angles formed by the radii to the tangency point prove that the lines are tangent.

~CS1

Mario's Parallel Coins

While playing a computer version of the classic Super Mario Bros. that I found online, I found a secret underground area, which is pictured above. In the underground area, I noticed that the coins seemed to be perfectly parallel to each other.

And, as it turned out, I was correct. By placing a point at the center of each coin and drawing lines between them, the coins formed lines parallel vertical lines and parallel horizontal lines. One can prove them parallel because the corresponding angles are congruent, the alternate interior angles are congruent, and the same-side interior angles are congruent. Because all of the angles formed by the intersections of the vertical and horizontal lines all have a measure of 90 degrees, they are perpendicular. This shows something important about coplanar horizontal and vertical lines: they are always perpendicular to each other. (~JC1)

Perfectly Perpendicular?

My family is currently renovating the kitchen, and the workers just put in the tile backsplash. Supposedly they have tools to make sure they place the tile perfectly, but I decided to see if it actually aligned. Surely if the tile was placed perfectly, then there should be a perpendicular line in between the tiles.

By definition, a perpendicular line is one that has a right angle (which is 90 degrees) on both sides. However, when I measured the angles of the tiles, it looks like the tile guys were a little off. One side is about 90.29 degrees and the other side is 89.71 degrees. It's pretty close but not perfect. Sorry guys but I just proved you wrong....It still looks really good though! (~JC2)

Parallel Bricks

These bricks demonstrate rectangles and, by definition, parallel lines. In fact, they demonstrate many of the postulates and theorems about parallel lines.

A rectangle is a special type of quadrilateral with opposite sides parallel and consecutive sides perpendicular. Because the consecutive sides are perpendicular, each consecutive angle must be a right angle and the opposite sides must be parallel because the same-side interior angles are supplementary. Each bricks is also parallel to the two next it, as shown above. (~JC1)

Parallel Lines and Bar Codes

The bar code on this eraser demonstrates Theorem 3-7, which states that in a plane two lines perpendicular to the same line are parallel.

Lines j and k are both in plane z, and they are both perpendicular to segment AB. Since they are both perpendicular to segment AB, the lines of the barcode are parallel. (~LSU)

Are We Blind to Parallel Lines?

This image is a picture of the blinds in my bedroom. It is an example of the theorem stating, "In a plane, two lines perpendicular to the same line are parallel." As you can see, line AE and line AF are both perpendicular to line CD. This makes line AE and line AF parallel to each other. - RG1

Perpendicular Lockers

Every day I go to the Morgan Hill Aquatics Center and put my swim bag in the locker rooms there.  We recently got new lockers and while examining them I noticed their perpendicular lines.  As you can see in the picture I put in GSP, I was able to prove that the locker lines formed 90 degree angles where they met.  Therefore, I now know that the lockers have perfect perpendicular lines! ~MG1