Introduction to Geometry (Level 2)

Introduction to Geometry (Level 2)

Alright in this post we are going to practice drawing, denoting and naming figures with a couple of examples, to be successful in geometry you need to be able to read and describe the basic building blocks of geometry both pictorially and symbolically. Let’s go over the first example:

Alright the first symbol represents a line segment since there is a line segment drawn directly above the letters. We can draw this segment by drawing two points P and Q and connecting them with a straight line as follows.

Remember line segments have a definite length they have a beginning and an end. They do not extend forever and ever in either direction.

The next symbol represents a line since there is line with arrows pointing in opposite directions drawn directly above the letters. This is similar to a line segment the only difference is that this line extends infinitely in both directions we show this by drawing arrows on both ends. So we first draw points P and Q and then we connect them making sure we draw arrows on both ends as follows.

The next symbol represents a ray. Since we have a line that extends in one direction drawn directly above the letters. The first letter in the symbol always represents the end point of the ray; keep this little detail in mind. So we first draw points P and Q and then draw an arrow that extends from point P towards point Q as follows.

It would be incorrect to draw this ray the other way around since the symbol is stating that the end point starts at point P not point Q.

The next symbol represents an angle for the most part we denote angles using three points, the middle letter always represents the vertex, so we go ahead and draw point P,Q and R, then we draw two rays both emanating from the vertex Q as follows.

You need to make sure that the vertex is being represented by the middle letter in this case point Q. It is very important to pay attention to these little details.

The final symbol represents a triangle, and like an angle it also requires three points, in this case each of the points will be connected by a line segment. So we first draw points P,Q and R, then we go ahead and connect them in the order represented by the symbol, so P connects with Q and Q connects with R and lastly you form the triangle by connecting point R and P.

Make sure you comfortable reading and drawing the various types of lines, rays, angles and triangles. Since you will be reading and drawing them extensively in your geometry class. It is important that you master this skill before we tackle more challenging problems in geometry. Alright now let’s practice denoting and naming geometric figures. Let’s move along to the next example.

Recall that lines contain arrows pointing in opposite directions and can be denoted by using two points in this example the line shown can be denoted by using point C and point D so we can name the line as “line CD or line DC” making sure we draw a line above the letters. Alternatively, we can also name this line as line since this line is also labeled with a lowercase letter. Keep in mind when we use two points to denote a line we usually want to express the points in alphabetical order, never the less both expressions are acceptable ways to name the line.

Alright let’s try the next example.

The following angle can be named in various ways, since this diagram only contains a single angle with point b as its vertex, we can use the vertex to name the angle in this case point E so we can name this angle as angle E making sure we draw the picture of an angle followed by the letter of the point that represents the vertex. Alternatively, the angle is also labeled with the number 5 so we can also name this angle as angle 5. We can also name angles by using 3 points in this case we can use point C E and D to name the angle, so we can name this angle as: angle CED or angle DEC making sure we write the point that represents the vertex in the middle. Just like lines we usually want to denote the points of an angle in alphabetical order whenever possible. Nevertheless both forms are acceptable ways to name this angle.

Alright let’s move along to the next example.

Here we have a triangle, recall that triangles contain 3 angles, hence the name triangle, this also means that triangles are formed by three sides. We can name the sides the same way we name line segments by using two points. In a triangle the points we will use are the once located on each vertex of the triangle. These vertices are essentially the end points of a line segment. The first side contains points R and S and can be named as segment RS or segment SR the second side contains points S and T and can be named as segment ST or segment TS and the third side contains points R and T and can be named as segment RT or segment TR or, Making sure we draw a line segment, to symbolically show that we are referring to a line segment not be confused with rays or lines.

Once again it is very important that you master this skill of drawing, denoting and naming figures. In the next post we will practice how to name and denote angles.