Introduction to Geometry (Level 4) | Naming Angles II

Introduction to Geometry (Level 4) | Naming Angles II

In this post we are going to continue denoting and naming slightly more challenging angles by using the points located on a geometric figure. Let’s go ahead and start with the first example.

Alright, we are asked to identify the vertex and sides of the given angles. Let’s start with the first angle. Angle 4 is located here and its vertex is represented by point C, now, the sides of the angle are formed by rays, CD and CB. Notice that Ray CB can also be named as Ray CA sine both points B and A are located on the same line segment, so this ray can be named in both ways, as long as you denote the vertex C first followed by point B or A.

Also notice that the arrows on each ray are not drawn in the figure, recall that the sides of an angle are technically formed by rays, when you name the sides of angles we usually name them as if they were rays, even though the ray is not explicitly drawn in the picture we still denote them as if they were rays.

In the same manner, let’s locate angle 1. Angle 1 is located here and its vertex is represented by point A, the sides of angle 1 are formed by ray AD which can also be denoted as ray AE the second side of the angle is formed by ray AB which can also be denoted as ray AC.

Lastly, let locate angle 6, Angle 6 is located here and its vertex is represented by point D, the sides of angle 6 are formed by ray DC and ray DB. Alright notice that the angles of this geometric figure are labeled with numbers which makes it slightly easier to reference a particular angle.

Alright, let’s move along to the next example.

Let’s first locate point B, Point B is located right here, at first glance it seems that there are two distinct angles that have point B as the vertex. The first of these angles is angle 3, notice that we can also name this angle as angle 3 or angle DBC or angle CBD, another that contains point B as the vertex is angle 2, we can also name this angle as angle 2 or angle DBA or angle ABD, it seems that those are all the angles, but the problem is asking us to name three angles, we all ready found two angles, now it’s just a matter of finding one more angle that has B as the vertex. At first, it might be hard to see but the third angle is formed by point C point B and point A. This angle usually referred to as a straight angle. You can think of this angle as the sum of angle 3 and angle 2. Straight angles will be discussed in more depth in a latter post for now keep in mind that these types of angles exist. With that said, we can name this angle as angle CBA or angle ABC.

Alright let’s try the final example.

Alright let’s take a look at point D, right of the bat it seems that there are three angles that contain point D as the vertex they include angle 7 which can be named as angle 7 or angle EDC or angle CDE, angle 6 which can be named as angle 6 or angle CDB or angle BDC, and angle 5 which can be named as angle 5 or angle BDA or angle ADB, these three angles are the obvious angles that have D as the vertex, but it turns out that there are 3 additional angles that contain point D as the vertex. The next angle is formed by the sum of angle 7 and 6, and can be named as angle EDB or angle BDE another angle is formed by the sum of angle 6 and 5, and can be named as angle CDA or angle ADC. The final angle is formed by the sum of angles 7, 6, and 5 and can be named as angle EDA or angle ADE, this is an example of straight angle we will talk about these types of angles in much later post. Going over these examples I want to point out the importance of developing your ability to see and identify the various angles that exist within a geometric figure. It is going to be vital as we tackle on more challenging problems in geometry.

Alright in our next post we will start going over examples that requires us to use concepts associated with sets such as unions and intersections of geometry figures.