Introduction to Geometry (Level 4)

In this video 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. Using the following figure find the following.

Name the vertex and the sides of the following angles: angle 4, angle 1, and angle 6.

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 since 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, lets 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. 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. Name three angles that have B as the vertex. 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 DBC or angle CBD. Another angle that contains point B as the vertex is angle 2, we can also name this

angle as: angle DBA or angle ABD. It seems that these 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 is 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 video 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. Name all the angles that have D as the vertex. 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 EDC or angle CDE. Angle 6 which can be named as: angle CDB or BDC, and angle 5 which can be

named as: 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 another example of a straight angle. 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 video we will start going

over examples that requires us to use concepts associated with sets such as unions and intersections

of geometric figures.

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