Download Triangles (Amanda)

Amanda Ferreira
October 11, 2007
Math 150
Geometry- Triangles
Math has always been a challenge for me, but geometry was the hardest. In high school,
I had to take geometry my sophomore year, and it was dreadful. I didn’t really learn anything,
except that I disliked math even more. The hardest thing for me was when we covered triangles
and had to figure out all the properties of triangles such as the lengths of sides, (equilateral,
isosceles, scalene), and then the properties of triangles with angles, (right, acute, and obtuse).
There is also another triangle that I never even heard of which is called an equiangular triangle
which is a triangle with three equal angles, which is surprising to me, because I thought my
teacher in high school went over all the different triangles, but it wasn’t even in our geometry
textbook. I guess I never really learned that much about triangles and the different ways to
classify them because my teacher just didn’t teach us how to figure it out. He never gave us any
knowledge on formulas or anything, so it was hard to know how to do equations and find
answers when there wasn’t any explanation. I had to figure out the degrees of angle for each
triangle and the measurements that each one would equal. I also had to figure out what the
vertex and altitude means when measuring a triangle. I suppose if I had been taught how to do
this, I would have still struggled with it, but not nearly as much as I am now. At least I would
have had the knowledge and formulas to actually sit down and try to figure them out, and if I
couldn’t understand how to figure them out ask someone to help me.
In order to figure out all the questions I had about triangles and all the different angles
and sides I had to do research and find books that had geometry in it, mainly about triangles,
with angles, sides, and measurements. Then I read through them and tried out some problems on
my own to see if I actually understood and knew what I was doing. It turned out not to be as
difficult as I originally thought it was, I just needed some time to actually sit down and have
examples that I could try to do out myself. The books I found on geometry were helpful, and
explained geometry and the triangles better than my teacher in high school did. I figured that
now as I thought about it, measurements of sides and angles of a triangle probably would have
been so much easier for me if I just tried to teach it to myself. If I wasn’t so frustrated, I bet I
would have tried. The things I was most confused with were the measurements to find the sides
and angles of each triangle and how each triangle was different in sides and lengths. This
confused me with all the numbers that we were supposed to add together, and it probably would
have helped if I had a formula to plug the numbers into, at least I could have tried to solve the
problem. I figured out that vertex is “the point of intersection of two sides. Informally, it is a
‘corner’ of the triangle (although the word corner properly refers to a right angle) (Burrell, 77). I
also learned that altitude is “(height) the perpendicular distance from a side to the opposite
vertex” (Burrell, 77).
The different triangles that are classified by the lengths of sides are equilateral, isosceles,
and scalene. An equilateral triangle has all sides that are equal in length, an isosceles triangle
has two sides that are equal and two angles that are equal, and a scalene triangle has no equal
sides or angles. The word congruent means that the triangles are the same shape and size. Each
triangle has different dimensions, such as different side lengths or different angles. Also all the
angles in a triangle add up to 180˚. The triangles are also classified by angles, such as a right,
acute, and obtuse. A right triangle has one right angle and the “sum of the measures of a right
triangle is 180˚” (Caron, 15). An acute triangle has three acute angles and each angle “is less
than 90˚, but they still add up to 180˚” (Caron, 15). An obtuse triangle “has one angle greater
than 90˚ and two angles that add up to less than 90˚” (Caron, 15).
After doing examples of each different length and angle, I tried different numbers and they all
came out to equal 180˚.
There is also a way to name the triangle; this can be done by “listing the vertices of the
angles in any way you choose. The symbol for a triangle is Δ” (Caron, 14). In any triangle there
are six ways to name it, “ΔBAC or ΔCAB, ΔCBA or ΔABC, ΔBCA or ΔACB” (Caron, 14).
There is also a way to name the three sides in a triangle: “side 1: CB or BC, side 2: CA or AC,
side 3: AB or BA” (Caron, 14). This can help and be less confusing, with each triangle and sides
named, it is easier to tell exactly what is meant when describing how to measure the triangle.
This was a good topic for me to work on. I now better understand the triangle
measurements and angles and sides. It’s really not as hard or as confusing as I thought it was
going to be. I actually enjoyed working out problems using different numbers that have to equal
180˚. I also liked learning all the different triangles and actually understanding why each
triangle is different. I am more comfortable with math and I now realize that if I actually sit
down and try examples it will be easier for me to understand. It also makes me feel less
frustrated because I now realize that I actually can do it if I just take the time to sit down and
really think and try different things until I figure out how it works.