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### Course: 4th grade (Eureka Math/EngageNY) > Unit 4

Lesson 4: Topic D: Two-dimensional figures and symmetry- Intro to reflective symmetry
- Identifying symmetrical figures
- Identify line symmetry
- Symmetry review
- Classifying triangles by angles
- Classifying triangles
- Worked example: Classifying triangles
- Classify triangles by angles
- Classify triangles by side lengths
- Types of triangles review
- Classifying shapes by line and angles types
- Quadrilateral properties
- Classifying shapes by lines and angles
- Classify shapes by line and angle types
- Polygons review
- Classify triangles by both sides and angles

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# Classifying triangles

The video explores how triangles are classified based on their sides and angles. It introduces the terms scalene, isosceles, and equilateral for side lengths, and acute, right, and obtuse for angles. It emphasizes that triangles can be categorized in multiple ways based on these characteristics. Created by Sal Khan.

## Want to join the conversation?

- What about reflex angles?(82 votes)
- A triangle cannot contain a reflex angle because the sum of all angles in a triangle is equal to 180 degrees. A reflex angle is equal to more than 180 degrees (by definition), so that means the other two angles will have a negative size.(52 votes)

- What if I had a isosceles triangle. Would it be a right angle?(20 votes)
- No, it can't be a right angle because it is not able to make an angle like that. It's no an eqaulateral.(20 votes)

- To remember the names of the scalene, isosceles, and the equilateral triangles, think like this!

Scalene: I have no rules, I'm a scale! My weight are always different!

Isosceles: I am an I (eye) sosceles (Isosceles)

Equilateral: I'm always equal, I'm always fair!(33 votes) - Why is an equilateral triangle part of an icoseles triangle.(15 votes)
- I've asked a question similar to that.

An equilateral triangle has all three sides equal, right?

But on the other hand, we have an isosceles triangle, and the requirements for that is to have ONLY two sides of equal length. That's why.(17 votes)

- Are all triangles 180 degrees, if they are acute or obtuse?(9 votes)
- Yes. All of the internal angles of a triangle equal 180 degrees.(15 votes)

- Um, the acute triangle at3:26. All of it's sides add up to 175, not 180. I checked on google. 60+61+54=175.(11 votes)
- That's just because Sal didn't draw a perfect triangle with completely straight lines and stuff. In a proper triangle, all the angles would add up to 180 degrees.(1 vote)

- What is a reflex angle? I've heard of it, and @ultrabaymax mentioned it. Maybe this is the wrong video to post this question on, but I'm really curious and I couldn't find any other videos on here that might match this question.(7 votes)
- Good question! A reflex angle is an angle measuring greater than 180 degrees but less than 360 degrees.

Have a blessed, wonderful day!(8 votes)

- An equilateral triangle has all three sides equal?

But on the other hand, we have an isosceles triangle, and the requirements for that is to have ONLY two sides of equal length.(7 votes)- An equilateral triangle has all three sides equal?

Answer: Yes

But on the other hand, we have an isosceles triangle, and the requirements for that is to have ONLY two sides of equal length.

Answer: Yes, the requirement for an isosceles triangle is to only have TWO sides that are equal. (e.g, there is a triangle, two sides are 3cm, and one is 2cm. That is an isosceles triangle. An equilateral triangle would have all equal sides.).(3 votes)

- Can an obtuse angle be a right.

Can a acute be a right to.

What type of isosceles triangle can be an equilateral.

An isosceles triangle can not be an equilateral because equilateral have all sides the same,but isosceles only has two the same.(4 votes)- An obtuse triangle cannot be a right triangle. A right triangle must have one angle equal to 90 degrees. All three of a triangle's angles always equal to 180 degrees, so, because 180-90=90, the remaining two angles of a right triangle must add up to 90, and therefore neither of those individual angles can be over 90 degrees, which is required for an obtuse triangle.

An acute triangle can't be a right triangle, as acute triangles require all angles to be under 90 degrees. A right triangle has to have one angle equal to 90 degrees.

All isosceles triangles are equilateral. The only requirement for an isosceles triangle is for at minimum 2 sides to be the same length. An isosceles triangle can have more than 2 sides of the same length, but not less. Equilateral triangles have 3 sides of equal length, meaning that they've already satisfied the conditions for an isosceles triangle.(10 votes)

- I do not understand this help! but thank you I am new.(4 votes)
- We can classify triangles using its sides or interior angles.

Sides:

- Equilateral (All sides equal)

- Isosceles (At least 2 sides equal)

- Scalene (No sides equal)

Interior Angles

- Right (1 Angle is 90 degree, i.e. Right angle)

- Obtuse (1 Angle is larger than 90 degree, i.e. Obtuse angle)

- Acute (No angle is larger than or equal to 90 degree)(7 votes)

## Video transcript

What I want to do in this video
is talk about the two main ways that triangles are categorized. The first way is based
on whether or not the triangle has equal sides,
or at least a few equal sides. Then the other way is
based on the measure of the angles of the triangle. So the first
categorization right here, and all of these are
based on whether or not the triangle has equal
sides, is scalene. And a scalene
triangle is a triangle where none of the
sides are equal. So for example, if I have
a triangle like this, where this side has length 3,
this side has length 4, and this side has
length 5, then this is going to be a
scalene triangle. None of the sides
have an equal length. Now an isosceles triangle is
a triangle where at least two of the sides have equal lengths. So for example, this would
be an isosceles triangle. Maybe this has length
3, this has length 3, and this has length 2. Notice, this side and
this side are equal. So it meets the constraint of
at least two of the three sides are have the same length. Now an equilateral
triangle, you might imagine, and you'd be right,
is a triangle where all three sides
have the same length. So for example, this would
be an equilateral triangle. And let's say that this
has side 2, 2, and 2. Or if I have a triangle like
this where it's 3, 3, and 3. Any triangle where all three
sides have the same length is going to be equilateral. Now you might say,
well Sal, didn't you just say that an
isosceles triangle is a triangle has at least
two sides being equal. Wouldn't an equilateral
triangle be a special case of an isosceles triangle? And I would say yes,
you're absolutely right. An equilateral triangle
has all three sides equal, so it meets the constraints
for an isosceles. So by that definition,
all equilateral triangles are also isosceles triangles. But not all isosceles
triangles are equilateral. So for example, this
one right over here, this isosceles triangle,
clearly not equilateral. All three sides
are not the same. Only two are. But both of these
equilateral triangles meet the constraint that
at least two of the sides are equal. Now down here, we're going
to classify based on angles. An acute triangle is a triangle
where all of the angles are less than 90 degrees. So for example, a triangle
like this-- maybe this is 60, let me draw a little
bit bigger so I can draw the angle measures. That's a little bit less. I want to make it a
little bit more obvious. So let's say a
triangle like this. If this angle is 60 degrees,
maybe this one right over here is 59 degrees. And then this angle right
over here is 61 degrees. Notice they all add
up to 180 degrees. This would be an acute triangle. Notice all of the angles
are less than 90 degrees. A right triangle
is a triangle that has one angle that is
exactly 90 degrees. So for example, this right over
here would be a right triangle. Maybe this angle or this angle
is one that's 90 degrees. And the normal way
that this is specified, people wouldn't just do the
traditional angle measure and write 90 degrees here. They would draw the
angle like this. They would put a little, the
edge of a box-looking thing. And that tells you that
this angle right over here is 90 degrees. And because this triangle
has a 90 degree angle, and it could only have
one 90 degree angle, this is a right triangle. So that is equal to 90 degrees. Now you could imagine an obtuse
triangle, based on the idea that an obtuse angle is
larger than 90 degrees, an obtuse triangle
is a triangle that has one angle that is
larger than 90 degrees. So let's say that you have a
triangle that looks like this. Maybe this is 120 degrees. And then let's see,
let me make sure that this would make sense. Maybe this is 25 degrees. Or maybe that is 35 degrees. And this is 25 degrees. Notice, they still add up to
180, or at least they should. 25 plus 35 is 60, plus
120, is 180 degrees. But the important
point here is that we have an angle that
is a larger, that is greater, than 90 degrees. Now, you might be
asking yourself, hey Sal, can a triangle be
multiple of these things. Can it be a right
scalene triangle? Absolutely, you could have
a right scalene triangle. In this situation
right over here, actually a 3, 4, 5
triangle, a triangle that has lengths of 3, 4, and
5 actually is a right triangle. And this right over here
would be a 90 degree angle. You could have an
equilateral acute triangle. In fact, all
equilateral triangles, because all of the angles
are exactly 60 degrees, all equilateral triangles
are actually acute. So there's multiple
combinations that you could have between
these situations and these situations
right over here.