Discussion for Triangles Discussion
You have learned about the following triangle parts and how they can be used to solve problems:
midsegment
circumcenter
incenter
point of concurrency
altitude
centroid
median
orthocenter
Reflect on each of these triangle parts and answer two of the following questions:
Which part of the triangle do you feel the most confident identifying and using? Why?
Which part of the triangle is the most challenging for you to identify and use? Why?
How might you use a perpendicular bisector or an angle bisector in your everyday life?
Post in the discussion with answers to these questions. Next, view posts from your classmates and respond to two of them. Do you feel confident about the same topic as your classmates? Why does this topic make sense to you? Do you share the same challenge as your classmates? If so, what can you do to overcome that challenge? Do you understand the examples your classmates provided of using a perpendicular or an angle bisector in everyday life? Do their examples apply to your life too?
I feel the most confident in identifying and using the median of a triangle. The median is simply a line segment that connects a vertex of a triangle to the midpoint of the opposite side. It is easy to identify because it is always located within the triangle and passes through the centroid. The median of a triangle has many useful properties, such as dividing the triangle into two equal areas and being a distance half of the longest side. I am confident in using the median to solve problems because I understand its properties and how it relates to the centroid.
On the other hand, the part of the triangle that is most challenging for me to identify and use is the circumcenter. The circumcenter is the point of concurrency of the perpendicular bisectors of the sides of a triangle. It is challenging for me to identify because it is not always located inside the triangle. Additionally, finding the circumcenter involves constructing perpendicular bisectors, which can be time-consuming and require accurate measurements. The circumcenter has properties such as being equidistant from the vertices of the triangle and serving as the center of the circumcircle, but I find it more difficult to directly apply these properties to solve problems.
A perpendicular bisector can be used in everyday life when constructing or aligning objects. For example, when hanging a picture, you can use a perpendicular bisector to find the center of the wall where the picture should be placed. By drawing a perpendicular bisector on the wall, you can easily find the point where the picture will be perfectly centered. An angle bisector can also be used in everyday life when determining the direction or path. For instance, if you are walking in a city and want to go in a certain direction, you can use an angle bisector to split the angle of the streets you are standing on, helping you to choose the correct path to take.