Hello, welcome to my next blog post! So this week in geometry class, we are learning about lesson 3-3 Proving Lines Parallel, 3-4 Perpendicular Lines, and 3-5 Slopes of Lines. These lessons can help us in our architect skills so that is why we are learning them.
Part of the problems given to us was to determine whether this diagram provide enough information to conclude to a||b. The vertical to 125 degrees is also 125 degrees. But since it is the supplementary of 55 degrees, then they same-side interior angles. Based on the converse of same-side interior angles, then a||b.
We also had to draw a figure in which the line segment AB is a perpendicular bisector of XY. However, we had to make XY NOT a perpendicular bisector to AB. This is what I drew:
Based on what I drew, the line segment AB is a perpendicular bisector of XY. Meaning, AB intersects XY in 90 degrees while one of AB's point is also XY's midpoint. However, XY is not a perpendicular bisector because it does not intersect line segment AB nor divides AB in half.
For the next topic, we had to think about a ladder. Have you ever noticed that all the rungs of a ladder or parallel? Maybe you did, maybe you did not. But the question is, "Why?"
After drawing all the ladder, I came into a conclusion as to why the rungs of a ladder are parallel. According to Theorem 3-4-3, if two lines are perpendicular to the same line, the the two lines are parallel to each other. In the ladder, all the rungs intersects both lines in 90 degrees. Because they are perpendicular to the same lines, then the rungs in the ladder are parallel.
Next, I've been challenged with a problem. The slope of line AB is greater than 0 and less than 1. I had to write an inequality for the slope of a line perpendicular to line AB. After solving the problem, I got the answer m < -1.
After that, I had to determine whether two cards are parallel if they were to drive the same speed and traveled the same distance. This is what I drew:
I concluded that since they traveled the same speed and distance, then they must be parallel because they both make a line.
This week, we've also learned about slope. In fact, there are two ways to find the slop of a line.
Based on this image, these are two ways to find the slope: the rise and run method, or the slope intercept formula.
After this, I had to draw two parallel lines and discuss how their slopes are similar.
The two red lines are in different points, however, they have the same slope.
Finally, I had to do something similar to the last photo, but this time with perpendicular lines.
In this photo, each perpendicular lines are in different points in each graph. Although, each line have the same slope.
