WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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For the next lesson, we are going to go over classifying triangles.
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Depending on the angles and the sides of the triangles, they have different names.
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First by angles, to classify, we know that we have three angles and we have three sides.
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Depending on the three angles of the triangle, we are going to have different names for them.
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The first one is called an acute triangle.
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Notice how all the angles, this angle here, this angle here,
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and this angle here, are all less than 90 degrees.
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It means that they are small; all angles are less than 90 degrees.
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Remember a 90 degree angle is a right angle.
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All three of them have to be less than 90.
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It is called an acute triangle.
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The next one is when you have one right angle.
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The other two angles are going to be acute.
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From within a triangle, if only one angle is a right angle, then it is called a right triangle.
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Only one angle is going to be 90 degrees.
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It is only one angle because you can only have one angle be a right angle.
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There is no way you can have a triangle where there is two angles that are right angles.
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Again a triangle can only have one right angle; you just can't do it.
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If that is one of the right angles of a triangle,
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if I draw this one as a right angle, that is not going to be a triangle.
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It is not possible to have two right angles in a triangle.
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Again one right angle; and that becomes a right triangle.
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The third type of triangle by its angles is an obtuse triangle.
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That means one of the angles, this one right here, is going to be greater than 90.
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One angle is greater than 90 degrees; this means bigger.
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One angle is bigger than 90 degrees; the other two are going to be acute.
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Just like the right triangle, it is impossible to have more than one angle of a triangle be obtuse.
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That is my obtuse angle.
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If draw another obtuse angle let's say like that, there is no way I can have a triangle.
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because remember a triangle only has three sides.
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You can only have one obtuse angle within a triangle.
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If you do have one obtuse angle, then it becomes an obtuse triangle.
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An acute triangle, a right triangle, and an obtuse triangle are all types of triangles by angles.
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A right triangle we know is when we have a right angle.
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To remember between an acute triangle and an obtuse triangle,
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think of what this spells: a-cute, a cute triangle.
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If these are small angles, then we tend to think that they are cute.
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You can think of it that way.
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Acute triangle is when all three angles are small so then it is a cute triangle.
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Obtuse is just a larger angle; that would be the obtuse triangle.
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Next is classifying triangles by size.
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Again depending on their sides, they are going to have different names.
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If all three sides are the same, then it is an equilateral triangle.
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These little marks right here, that shows that it is the same.
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If this side, this side, and this side all have one mark each,
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that means all three sides are the same, are congruent.
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That means this is an equilateral triangle.
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If this is 10 inches, then this has to be 10 inches and that has to be 10 inches.
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It is equilateral; this means equal; lateral means side.
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It is like equal sides; equilateral triangle.
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Three sides are congruent; three sides are the same.
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Isosceles triangle, the next one.
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Isosceles is when you have two out of the three sides being the same.
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This side and this side are congruent; congruent just means the same.
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This side and this side are the same; that is an isosceles triangle.
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This is all three sides; this is two out of the three sides.
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Two sides are the same.
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The third one is a scalene triangle.
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A scalene triangle is when no sides are the same.
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This one, this one, and this one, they are all different.
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All sides are different; scalene; equilateral, isosceles, and scalene triangle.
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This is classifying triangles by its sides, depending on the sides.
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The first example is to classify the triangle by its angles and sides.
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Look at the angles first.
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If you look at the angles, this is an acute angle.
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This is an acute angle; and this is an acute angle.
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We can tell it because they are all smaller than 90 degrees.
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They are all smaller than right angles.
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That name for a triangle with all three acute angles is an acute triangle.
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By sides, look at the sides.
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This one is congruent to this one is congruent to that.
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All three sides are the same; that is an equilateral triangle.
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This is by angles; this is by sides; this type of triangle has two names.
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This one, this is acute, acute, and acute; therefore this is an acute triangle.
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By its sides, we have two that are the same so this is isosceles triangle.
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Angles and sides; let's sketch each figure; an isosceles right triangle.
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We have to make sure that it is... isosceles is when we have two sides being the same.
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A right triangle is when we have one right angle.
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I need to draw a triangle with one right angle and these sides being the same like that.
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Just to mention, if this is a right isosceles triangle, we know that this is 90 degrees.
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Then this angle and this angle will actually be exactly the same because this is isosceles.
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See how the distance from here to here and from here to here are the same.
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This angle and this angle will be exactly the same also.
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This is an isosceles right triangle.
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The next one is scalene and obtuse triangle; a scalene obtuse triangle.
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Scalene is when no sides are the same.
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Obtuse is when you have one angle that is larger than 90.
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Obtuse angle; and then scalene means that no two sides are the same.
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Draw one short; draw one longer; this one is going to be the longest.
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That is a scalene obtuse triangle.
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Classify the triangle by its angles and sides.
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Here my angles first; let's do angles; let's see; this is acute.
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This looks like it is obtuse because it looks like it is greater than 90.
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This is acute.
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Just because I have one obtuse angle, that is going to make this whole triangle an obtuse triangle.
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By its sides, we have two sides that are the same.
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This is going to be an isosceles triangle; obtuse triangle and isosceles triangle.
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The next one, by its angle, I have one right angle; acute and acute angle.
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When you have only one right angle, that makes the whole triangle a right triangle.
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By its sides; it doesn't show that any two sides are the same.
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Looks like this is the shortest one.
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This is the next one; that one is the longest.
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This is going to be scalene; scalene triangle.
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For the fourth example, given the measures of the angles of a triangle,
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classify the triangle by its sides and measures.
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Here just based on the angle measures, we need to figure out
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what type of triangle it is by its angles and by its sides.
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Here look at that; that is a 90 degree angle.
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That means I am going to have a right triangle.
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This is 90; the other two angles are going to be 45 and 45.
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If I were to draw this like that, like a house, this is 45 and this is 45.
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They are the same.
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That means these two sides are going to be the same
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because the distance from here to here and the distance from here to here
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have to be the same for these two angles to be the same.
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This is going to be an isosceles right triangle.
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This is by its sides; this is by its angles.
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The next one, 30 degrees, 100 degrees, and 50 degrees.
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If you look at that one, that is greater than 90; greater than 90.
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Let me just draw this again so that way you can see this a little bit clearer.
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This will be the 100 degree angle.
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This is going to be the 100 degree angle.
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Notice how I drew this side really long and this side really short.
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If I draw this really long, then see how this angle gets skinnier so it gets less.
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That means that one is going to be the 30 degree one and this one is going to be the 50 degree one.
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In order for me to have different angle measures for this one and this one,
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these two sides have to be different because I have to draw one long so it gets skinnier.
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Then my angle would be less; it would be smaller.
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This we know first of all is going to be an obtuse triangle.
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But with the sides, because I had to draw one long, one longer than the other
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so the angle would be smaller than the other, it is going to be a scalene triangle.
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This is a scalene obtuse triangle.
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Scalene by its sides; obtuse because of that 100 degree angle.
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That is it for this lesson; thank you for watching Educator.com.