All language subtitles for English (auto-generated)_en_0_Types of Triangles in Euclidean Geometry(1080P_HD)

Professor Dave here. Let's learn about

different types of triangles. He knows a

lot about all kinds of stuff. Professor

Dave explains.

We know that if we connect three line

segments, we can create a simple shape

called a triangle. But in what way will

these lines connect? And what are the

different types of triangles that will

result?

Let's go through a list of the most

common types of triangles now.

First, a few general definitions. Since

we know what acute, obtuse, and right

angles are, we can then learn about

acute, obtuse, and right triangles.

Acute triangles have angles that are all

acute, or less than 90°. An obtuse

triangle has one obtuse angle, or more

than 90°. And a right triangle has one

right angle.

As we can see by looking at the angles

in these triangles, and every other

triangle we could possibly draw, the

angles in a triangle will always add up

to 180°.

This is why any triangle can have at

most one right or obtuse angle, because

two of them would add up to 180 or more,

and then there is nothing left for the

third angle.

This fact will help us algebraically

determine the measures of certain angles

later.

Triangles can be classified not just by

angles, but also by side lengths.

A scalene triangle is defined as having

three sides of different lengths.

An isosceles triangle has two sides out

of the three that are exactly the same

length, and therefore two angles that

are precisely the same measure.

Specifically, the two angles that are

opposite the two identical sides.

And an equilateral triangle has all

three sides of the same length, and

therefore three identical angles.

Since the three identical angles must

add up to 180°,

each angle must therefore be 60° in an

equilateral triangle.

Every triangle must be one of these

three types, because if they have three

sides, it must either be the case that

they are all the same,

two are the same, or none are the same,

as those are all the options we have.

It's worth our time to also quickly

mention some special kinds of right

triangles. One is the 45-45-90 triangle.

This will have two legs of equal length

X, and a third side, a hypotenuse, of

length X root 2.

There are also 30-60-90 triangles, and

these have sides of length X, X root 3,

and 2X.

Now that we are equipped with all of

this information, we should be able to

look at a diagram like this and fill in

all the missing angles. We just fill

them in one at a time by using the rules

we know. If we have one of two vertical

angles, the other will be the same as

the first. If we have two angles in a

triangle, then the third will be 180

minus the other two.

If we have one of two adjacent angles,

the other will be 180 minus the first,

as these are supplementary, such as with

the case of an exterior angle like this

one. The exterior angle will also be

equal to the sum of the other two angles

in the triangle, since this one plus the

exterior angle equals 180, and this one

plus the other two also equals 180. So,

these values must be equal.

This kind of reasoning is the essence of

geometry. All we are really doing is

drawing pictures in the sand like the

Greeks did, and asking questions about

them. What can and can't be true about

these shapes?

It's like a playground for the brain,

and if we follow the rules of the

playground, we get meaningful answers to

questions.

These kinds of rules, like the ones that

dictate angle relationships, will be

applied constantly during our study of

geometry. So, let's check comprehension.

Thanks for watching, guys. Subscribe to

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content. And as always, feel free to

email me,

professordaveexplains@gmail.com.