Goal: The goal of this unit is for students to be able to
Define parallel and perpendicular lines
In order to say that two lines have the property of being 'parallel', the two lines must both go in the same direction and can not cross eachother, ever.
In order for two lines to be 'perpendicular', the two lines
must not only cross, but they must do so at one exact location and will never ever cross again.
In addition, they must form a perfect corner or 90°
angle at the intersection of the two lines.
Before we get too far ahead of ourselves, let's look at some examples of every day objects that possess both parallel and perpendicular properties.
Can you look at each image below and locate the parallel lines? The Perpendicular lines?
In the first image with the cofee cup, I am seeing parallel lines when I look at the ends of the three books under the cofee cup. The top and bottom of each book in the stack is parallel to the other tops and bottoms of the books.
I also notice the window sill in the background; the right and left sides are parallel, while the bottom board in the windown would be considered perpendicular to the left and right sides.
When looking at the skyscraper, I see both parallel and perpendicular lines. Looking in the same direction as the photo was taken, I see the vertical beams rising up into the cloudy sky. These beams are all parallel to eachother. However, the beams that run left to right are perpendicular to the previously mentioned vertical beams.
At this point in time, It would be fair to say that lines going up and down are always perpendicular to lines that are going left to right.
The third building in the images is weird but amazing. The horizontal lines that make up the railing around the banister and around the building seem to be indicative of parallel lines.
But it is not true in this case becasause the fact that the railing will complete a full circle around the building then meet on the other side to form one solid ring around the whole building.
In our definition of parallel lines we will add on a rule to exclude buildings like these due to not being within the rules of Geometry. Two lines are parallell if they never intersect. The circular portions defeat the idea of parallel.
Looking at the fourth photo, I will now let you decide. Are the lines parallel, perpendicular, or neither? When you are ready, select your answer and see if you were right!
If you try all three buttons, you will find out something
suprising about this architectural structure.
One main issue with the last image: there are parallel, perpendicular, and neither in the image. So you could chose all three answers and still get the right answer! 😇
