Blog Entry #4 (Parallel Lines, Perpendicular Lines, and Slopes)

          Hey! This weeks blog topics consist of three sections (3-3, 3-4, and 3-5). I am super excited to talk about parallel lines, perpendicular lines, and slopes. I have learned a lot of new topics in my geometry class that I want to share with you! I was assigned to do 8 questions in total.

First off, on pg. 168 I did number 42. Yes, the information given in the diagram does allow me to conclude that a ll b. If you look at the angles you can actually see that it is a vertical angle (I drew it out which helped me a lot). Because they are vertical angles it means that the angles are congruent. Therefore, it tells me that the angle opposite of 125 degrees is also 125 degrees. Now we are not stopping there, the angles on the opposite side are 55 and 125 degrees. Now, if you add them together 55 + 125 = 180. You get 180 degrees! This means that they are supplementary. The converse of the same-side interior angles theorem helps me verify my statement.  

Next, I was assigned to do pg. 177. I answered numbers 27 and 28.

#27

         As you can see from the picture above, AB is the perpendicular bisector of XY, but XY is not the perpendicular bisector of AB. 

        #28   Because it specifies that it is PERPENDICULAR, you know that it is 90 degrees. This means the other sides are also 90 degrees. Because of the congruence of the sides, you know it is parallel. I applied the same concept as in Theorem 3-4-3, it is just that there is more than two coplanar lines. The theorem helped me validate my statement.

On pg. 186 I answered numbers 23 and 24. The answer for #23 is the reciprocal of the given.

        

                                   #23                                      

         

          #24 The two cars are at the same speed. I know that they both have the same slope. Remember parallel lines have the same slope. I know that they are the same!

Answering Ms. Buenaflors Questions: Part 2 

         The first way you can determine the slope of a line is using the slope formula. You take your coordinates and substitute it in your formula. The slope formula is y-coordinates over x-coordinates. You subtract. That is the first way to determine the slope of a line. 

          The second way you can determine the slope of a line is by using the rise over run formula. 

In the example below, my coordinates were (0,6) and (6,0). I went ahead a plotted them. After i plotted my points, I drew a line through them. Now I have a slope triangle. I counted the boxes (I used quad paper), because I counted down the boxes on my quad paper; my rise was -6. Now for my run, I counted to the right. Therefore, my run would be 6. Now -6 divided by 6 equals to -1. My slope is -1. Now if I tried to find the slope using the slope formula it would also equal to -1. 

USING RISE OVER RUN FORMULA:

USING SLOPE FORMULA:

           In the picture below, two coplanar lines are perpendicular to the same line. The parallel lines and perpendicular lines slopes are related because parallel lines have the same slope, and perpendicular lines slope is the reciprocal. If the slope is 1 the reciprocal of that would be -1. 

          Whewwww! I went through a lot of topics in this blog post. It was pretty confusing and hard to wrap my mind around at the beginning. Practice really does make perfect. Now I am much more confident in topics such as parallel and perpendicular lines. I am still improving and learning more about slope. I am really happy about the outcome of this geometry blog post!