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Classifying Triangles

Related Links

  • Acute triangles’ angles are all acute
  • Right triangles have one right angle
  • Obtuse triangles have one obtuse angle
  • Equilateral triangles have equal side lengths
  • Isosceles triangles have two equal side lengths
  • Scalene triangles’ sides do not equal each other

Classifying Triangles

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Types of Triangles by Angles 0:05
    • Acute Triangle
    • Right Triangle
    • Obtuse Triangle
  • Classifying Triangles by Sides 4:18
    • Equilateral Triangle
    • Isosceles Triangle
    • Scalene Triangle
  • Extra Example 1: Classify the Triangle by Its Angles and Sides 6:34
  • Extra Example 2: Sketch the Figures 8:10
  • Extra Example 3: Classify the Triangle by Its Angles and Sides 9:55
  • Extra Example 4: Classify the Triangle by Its Angles and Sides 11:35

Transcription: Classifying Triangles

Welcome back to

For the next lesson, we are going to go over classifying triangles.0001

Depending on the angles and the sides of the triangles, they have different names.0008

First by angles, to classify, we know that we have three angles and we have three sides.0016

Depending on the three angles of the triangle, we are going to have different names for them.0025

The first one is called an acute triangle.0034

Notice how all the angles, this angle here, this angle here,0039

and this angle here, are all less than 90 degrees.0044

It means that they are small; all angles are less than 90 degrees.0050

Remember a 90 degree angle is a right angle.0064

All three of them have to be less than 90.0067

It is called an acute triangle.0072

The next one is when you have one right angle.0076

The other two angles are going to be acute.0083

From within a triangle, if only one angle is a right angle, then it is called a right triangle.0087

Only one angle is going to be 90 degrees.0097

It is only one angle because you can only have one angle be a right angle.0104

There is no way you can have a triangle where there is two angles that are right angles.0110

Again a triangle can only have one right angle; you just can't do it.0118

If that is one of the right angles of a triangle,0126

if I draw this one as a right angle, that is not going to be a triangle.0129

It is not possible to have two right angles in a triangle.0133

Again one right angle; and that becomes a right triangle.0138

The third type of triangle by its angles is an obtuse triangle.0143

That means one of the angles, this one right here, is going to be greater than 90.0149

One angle is greater than 90 degrees; this means bigger.0158

One angle is bigger than 90 degrees; the other two are going to be acute.0164

Just like the right triangle, it is impossible to have more than one angle of a triangle be obtuse.0172

That is my obtuse angle.0182

If draw another obtuse angle let's say like that, there is no way I can have a triangle.0186

because remember a triangle only has three sides.0191

You can only have one obtuse angle within a triangle.0196

If you do have one obtuse angle, then it becomes an obtuse triangle.0201

An acute triangle, a right triangle, and an obtuse triangle are all types of triangles by angles.0207

A right triangle we know is when we have a right angle.0220

To remember between an acute triangle and an obtuse triangle,0224

think of what this spells: a-cute, a cute triangle.0229

If these are small angles, then we tend to think that they are cute.0237

You can think of it that way.0242

Acute triangle is when all three angles are small so then it is a cute triangle.0244

Obtuse is just a larger angle; that would be the obtuse triangle.0249

Next is classifying triangles by size.0257

Again depending on their sides, they are going to have different names.0262

If all three sides are the same, then it is an equilateral triangle.0267

These little marks right here, that shows that it is the same.0275

If this side, this side, and this side all have one mark each,0280

that means all three sides are the same, are congruent.0285

That means this is an equilateral triangle.0291

If this is 10 inches, then this has to be 10 inches and that has to be 10 inches.0293

It is equilateral; this means equal; lateral means side.0297

It is like equal sides; equilateral triangle.0304

Three sides are congruent; three sides are the same.0310

Isosceles triangle, the next one.0322

Isosceles is when you have two out of the three sides being the same.0324

This side and this side are congruent; congruent just means the same.0332

This side and this side are the same; that is an isosceles triangle.0338

This is all three sides; this is two out of the three sides.0343

Two sides are the same.0347

The third one is a scalene triangle.0355

A scalene triangle is when no sides are the same.0358

This one, this one, and this one, they are all different.0363

All sides are different; scalene; equilateral, isosceles, and scalene triangle.0367

This is classifying triangles by its sides, depending on the sides.0386

The first example is to classify the triangle by its angles and sides.0396

Look at the angles first.0402

If you look at the angles, this is an acute angle.0405

This is an acute angle; and this is an acute angle.0408

We can tell it because they are all smaller than 90 degrees.0411

They are all smaller than right angles.0414

That name for a triangle with all three acute angles is an acute triangle.0419

By sides, look at the sides.0435

This one is congruent to this one is congruent to that.0438

All three sides are the same; that is an equilateral triangle.0442

This is by angles; this is by sides; this type of triangle has two names.0452

This one, this is acute, acute, and acute; therefore this is an acute triangle.0461

By its sides, we have two that are the same so this is isosceles triangle.0474

Angles and sides; let's sketch each figure; an isosceles right triangle.0487

We have to make sure that it is... isosceles is when we have two sides being the same.0499

A right triangle is when we have one right angle.0506

I need to draw a triangle with one right angle and these sides being the same like that.0512

Just to mention, if this is a right isosceles triangle, we know that this is 90 degrees.0527

Then this angle and this angle will actually be exactly the same because this is isosceles.0536

See how the distance from here to here and from here to here are the same.0542

This angle and this angle will be exactly the same also.0549

This is an isosceles right triangle.0555

The next one is scalene and obtuse triangle; a scalene obtuse triangle.0558

Scalene is when no sides are the same.0564

Obtuse is when you have one angle that is larger than 90.0570

Obtuse angle; and then scalene means that no two sides are the same.0577

Draw one short; draw one longer; this one is going to be the longest.0584

That is a scalene obtuse triangle.0589

Classify the triangle by its angles and sides.0598

Here my angles first; let's do angles; let's see; this is acute.0602

This looks like it is obtuse because it looks like it is greater than 90.0610

This is acute.0618

Just because I have one obtuse angle, that is going to make this whole triangle an obtuse triangle.0619

By its sides, we have two sides that are the same.0634

This is going to be an isosceles triangle; obtuse triangle and isosceles triangle.0638

The next one, by its angle, I have one right angle; acute and acute angle.0651

When you have only one right angle, that makes the whole triangle a right triangle.0660

By its sides; it doesn't show that any two sides are the same.0671

Looks like this is the shortest one.0677

This is the next one; that one is the longest.0679

This is going to be scalene; scalene triangle.0683

For the fourth example, given the measures of the angles of a triangle,0696

classify the triangle by its sides and measures.0701

Here just based on the angle measures, we need to figure out0708

what type of triangle it is by its angles and by its sides.0719

Here look at that; that is a 90 degree angle.0725

That means I am going to have a right triangle.0728

This is 90; the other two angles are going to be 45 and 45.0734

If I were to draw this like that, like a house, this is 45 and this is 45.0742

They are the same.0752

That means these two sides are going to be the same0754

because the distance from here to here and the distance from here to here0759

have to be the same for these two angles to be the same.0765

This is going to be an isosceles right triangle.0772

This is by its sides; this is by its angles.0785

The next one, 30 degrees, 100 degrees, and 50 degrees.0790

If you look at that one, that is greater than 90; greater than 90.0797

Let me just draw this again so that way you can see this a little bit clearer.0812

This will be the 100 degree angle.0826

This is going to be the 100 degree angle.0831

Notice how I drew this side really long and this side really short.0837

If I draw this really long, then see how this angle gets skinnier so it gets less.0843

That means that one is going to be the 30 degree one and this one is going to be the 50 degree one.0850

In order for me to have different angle measures for this one and this one,0855

these two sides have to be different because I have to draw one long so it gets skinnier.0861

Then my angle would be less; it would be smaller.0868

This we know first of all is going to be an obtuse triangle.0873

But with the sides, because I had to draw one long, one longer than the other0879

so the angle would be smaller than the other, it is going to be a scalene triangle.0883

This is a scalene obtuse triangle.0888

Scalene by its sides; obtuse because of that 100 degree angle.0900

That is it for this lesson; thank you for watching