For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

## Discussion

## Study Guides

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## Table of Contents

## Transcription

## Related Books

### 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

### Basic Math Online Course

### Transcription: Classifying Triangles

*Welcome back to Educator.com.*0000

*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 out*0708

*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 same*0754

*because the distance from here to here and the distance from here to here*0759

*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 other*0879

*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 Educator.com.*0908

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