Introduction to Geometry (Level 2)

Alright in this video 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:

Draw a figure that represents the following symbols. Line segment PQ, line PQ, Ray PQ, angle PQR, and trianlge PQR.

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.

What are the three possible names for the

line shown?

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 directly

above the letters. Alternatively, we can also

name this line as line l 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

What are four possible names for the angle

shown?

The following angle can be named in various

ways, since this diagram only contains a single

angle with point E 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 try the next example.

Name the sides of triangle RST.

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:

line segment RS or line segment SR the second side contains

points S and T and can be named as: line segment ST

or line segment TS and the third side contains points

R and T and can be named as: line segment RT or line segment TR, 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 our next video we will

practice how to name and denote angles.

Ur really good. Can u make videos about triple intergals plz

The goal is to expand the library of videos to include that topic and much more! Unfortunately we can only generate one video every week at our current capacity. You can help out by spreading the word about Math Fortress.

Is it a company?

Not yet. We are planning of expanding the library on one math topic, we are analyzing to see which math topic is in demand.

I cried in geometry class today, I wasn't understanding anything. So I decided to find help on here good thing I did I was begining to worry how I was going to pass. Thank you very much for helping me have a better understanding.

…MATH FORTRESS 2!!! … anyway these videos are great, I'm learning a lot, I have to take a college assessment soon and i want to get a high score on the math portion of it 😀

This shit turns me on!

can you do geometry ;ike transformations

i think I'm starting to understand. wow so what am i going to school for if a video is showing me better.

this is really helpful since im not exactly the best at math. thanks for making these videos

So I can't name the angles as: ∠CED, ∠C5D, ∠DEC, ∠D5C, ∠E and ∠5?

If not: why?

Thanks for the videos 🙂

realy helpful

Great quality and very useful. Thank you!

very well done

Wow very helpful

grear

How can you determine so easily that the angle PQR is made up of rays and not segments or lines? at mark 2:19?

VERY GOOD.

0:23 Example 1

3:24 Example 2

4:13 Example 3

5:18 Example 4

you teach better than my teacher

Thanks

Your videos are so much understanding. My geometry teacher teaches us nothing, but gives us notes.

Because of you, I’ll be better at geometry. Thank you!

Awesome thnks excellent teacher couldn't find better

Wish I had YouTube when I was in school lol

Geometry is soooo much easier than algebra😩😩

does an angle always go on forever tho???

this video is amazing cuz im dum ass fuck

I'm starting Geometry Honors in the 9th grade, which is in 2 months. This video was a good starting point to learn the basics.