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 intersecting lines and angle measures.
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Remember a line is always straight and it is never ending.
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Meaning it goes on forever; that is what these arrows are for.
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It shows that it is going on forever this way and that way.
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To name a line, we can use the points that are on the line.
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To name a line using the points, we need at least two points.
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Here point A and point B; can write it as A, B.
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Then you are going to draw a little line above it like that.
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That shows line AB.
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Because it doesn't matter which way it is going,
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whether I name it AB or BA, I am still talking about the same line.
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It goes on forever in both directions.
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I can also say BA with a line over it to show that it is a line.
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This is how you represent, how you name this line.
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This whole thing is also called L; I can also name this as line L.
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When you usually name a line, it is usually in cursive.
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That is why it is a cursive L; line L.
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Three ways; AB using the points, two points on the line.
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AB with the line above, AB; or BA, same thing.
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Or if the whole thing has a name L, then you can just call it line L.
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When you have two lines that are intersecting or two lines
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that cross each other like this, they are intersecting lines.
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They are two lines that intersect; they intersect at point P.
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This is a point; that is the point where they touch; that is point P.
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This is line L; line N.
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For this, you can also name this as line CD; line DC just like we did here.
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But P is also on that line; I can also name this as line PD; PD with a line above it.
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That can also be used to name this line; just any two points on that line.
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If I say line CD or line PD, I am talking about the same line.
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It doesn't matter which one.
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Again that is intersecting lines, when they cross each other.
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For angles, this right here is an angle; B is a point on one side.
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C is a point on the other side of the angle; there is two sides.
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This point right here where those two sides meet, that is the vertex.
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That is called the vertex; point A is the vertex of that angle.
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When I name this angle, I can say angle; that just shows an angle.
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I use the points; I need three points on this angle.
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If I just say BC, then that doesn't tell me what angle I am talking about.
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Or that doesn't even give me an angle; I have to say BAC; angle BAC.
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Again if you are going to use points to represent the name of an angle, then you have to use three points.
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I can also say angle CAB.
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Make sure your angle is going like that; it is not going like this.
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If you noticed for these two names, both of these, A the vertex is the middle point.
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It is BAC; angle CAB; I can't say angle BCA.
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Angle BCA is not the correct name for it.
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Angle BCA, that is not a name for this angle.
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The vertex has to be the middle point when you name it.
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Another name, just like the previous slide where we had line L,
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the name of the line was L so we can also name it line L.
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For this one, if it says 1, usually the angles, if there is a name for it, it is a number.
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That number 1 right there, that is talking about this angle.
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So I can also say angle 1.
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The degree of an angle is the angle measure.
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Measure is talking about how narrow or how wide open the angle is.
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This right here, if I say this is a 90 degree angle, it is a perfect right angle.
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Meaning this is vertical and this is horizontal.
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This little box right here says that it is a 90 degree angle.
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This is 90; to represent degree is a little dot right there.
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That is 90 degrees.
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If I have a straight line, a straight line measures 180 degrees
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because it is like 90 and then it is another 90.
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If I were to draw a 90 degree angle from here, it will be half way.
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This is 90; this is 90; together it makes 180.
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If I start from here and I go all the way around a full circle, that is 360.
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You can also use this to represent a 360.
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This right here was 180; that is 180.
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This again is 180; together it is 360.
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All of it together, the whole full circle going all the way around,
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from starting point and then going all the way back to that same point, it is 360 degrees.
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Again right angle is 90.
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Two right angles make a straight line; that is 180 degrees.
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Two straight lines, going this way and then going another this way, is 360.
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That is a full circle; a full circle is always 360 degrees.
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There is three types of angles when it comes to classifying.
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The three types would be acute angle... this is when...
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Remember this is a 90 degree angle; that is a 90 degree angle.
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Acute angle has to be smaller than a right angle.
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It has to be smaller than 90; this is less than 90 degrees.
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That makes up an acute angle.
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Right angle we know is perfectly 90 degrees.
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An angle that is greater than 90, greater than 90 degrees, is called an obtuse angle.
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The right angle would be like that right there; this is 90.
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It is going more than 90; it has to be bigger than 90.
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These are the three types of angles.
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So that you don't confuse the acute angle with the obtuse angle, we know a right angle is perfectly 90.
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Acute angle and an obtuse angle; notice how the acute angle is a lot smaller than the obtuse angle.
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Acute angles are small; they are smaller than 90.
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Think of it as a cute angle because it is small.
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Acute angles are small; obtuse angles are big; three types of angles.
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When we compare two different angles to each other, some angles have a relationship.
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The first angle relationship is a vertical angle.
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If we have intersecting lines, two lines that are intersecting, there is four angles that are formed.
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We have this angle, this angle, this angle, and this angle.
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There is four angles that are formed by intersecting lines.
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When you look at the opposite angles, the top one and the bottom one, those are called vertical angles.
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Remember when we talked about how to name angles.
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This is angle 1; this is angle 2.
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We can name angles by using the points on the angle.
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Or if it is labelled as 1, 2, then we can say that that is angle 1 and this is angle 2.
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This is different; don't get it confused with angle measure.
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Because angle measure, that is how many degrees that angle is and it has that little degree sign.
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This is not degrees; it is not 1 degree.
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It is angle 1; this is angle 2.
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Angle 1 and angle 2 are vertical angles; that is the relationship between the two.
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Again if they are intersecting lines and then they are opposite, this one and this one are vertical angles.
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This one and this one are also vertical angles.
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If this is angle 3, this is angle 4, then angles 3 and 4 would also be vertical angles.
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The next type of relationship is called adjacent angles.
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Adjacent, think of it as next to.
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They are angles that are next to each other.
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They have to have a common vertex and side; they share two things.
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The vertex, we know that a vertex is this part right here.
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That is the vertex; they have to have the same vertex and a side.
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Angles 1 and 2 here are adjacent because they are next to each other.
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This is the vertex of angle 1; this is the vertex of angle 2.
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They have the same vertex; and they share a side.
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This is the side that they share; these would be adjacent angles.
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Adjacent angles don't always have to be from intersecting lines.
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If I have let's say like this, angles 1 and 2, these would be adjacent angles
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because they share the same vertex and the same side and they are next to each other.
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Same vertex; same side; angles 1 and 2 here are also adjacent.
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Complementary angles.
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Complementary angles are two angles that when you add them together becomes 90.
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It has to be 90 for it to be complementary.
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Again two angles that add up to 90 degrees.
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Here angle 1 and angle 2, if you add them together, it is going to become 90 degrees.
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If I were to take this angle and place it so that it is like this, this would be angle 1.
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See how it forms a right angle; 90 degrees is a right angle.
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Any two angles that add up to 90; they don't all have to be adjacent.
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It doesn't have to be like this for it to be complementary.
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I can have one angle here; I can have another angle over here somewhere.
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As long as they add up to 90 degrees, they would be complementary angles.
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Supplementary angles are any two angles that add up to 180.
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Here angle 1 and angle 2 would add up to 180.
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If I were to put it together, notice how they would line up to be a straight line.
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This is angle 1; this is angle 2.
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If you add them together, see how this would be a straight line, 180 degrees.
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Remember how we said if I have a straight line, it is as if I have two 90 degree angles.
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This is 90; this is 90; together they add up to 180.
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A straight line is 180.
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If I have two angles that form a straight line, then they are supplementary angles.
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They don't have to be together; they don't have to be adjacent.
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They can be just like the complementary angles.
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They can be two angles that are split; one angle here, one angle over there.
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As long as they add up 180, they are supplementary angles.
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Again two angles that are opposite to each other when they are
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formed by intersecting lines are called vertical angles.
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Angles 1 and 2, since they are opposite angles, they are vertical.
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Adjacent angles are two angles that are next to each other.
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They have to share a common vertex and a side.
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An example of nonadjacent angles, meaning two angles that are not adjacent, would be like that.
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This is angle 1; this is angle 2.
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Even though they are next to each other, they are not adjacent because they don't share the same vertex.
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This is the vertex of angle 1; this is the vertex of angle 2.
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For this, this is not adjacent.
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They have to be next to each other and share the same vertex.
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Complementary angles are two angles that add up to 90 whether they are together, adjacent, or not.
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Supplementary angles are two angles that add up to 180 whether or not they are adjacent.
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To remember between complementary and supplementary, C comes before S in the alphabet.
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C, A-B-C, and then S is way down there; C comes before the S.
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90 comes before 180 if you were to count; 90 comes before 180.
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C before S; 90 before 180.
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C, complementary angles are 90 degree angles; supplementary are 180.
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That is just one way for you to remember between complementary and supplementary.
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Our examples, the first one, write two other names for AB, line AB.
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Line AB is this line right here.
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To find two other names... I didn't label them; this is L, N, and P.
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Here I can say, since that is AB, I need to find two other names.
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I can say BA; line BA; that is one other name.
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Then I can say line P; line P.
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Again the names for lines are usually in cursive; line BA and line P.
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Name two intersecting lines; line AB and line AC are intersecting.
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Line AB with line DE is intersecting.
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I can also say line P with line L or line P with line N; any of those.
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But just make sure that it is not line AC with line DE.
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They could intersect eventually because remember these lines are never ending.
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They go on forever; if they are not parallel, eventually they can meet sometime.
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But in this diagram, it doesn't show them intersecting.
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We can just say line AB with a line; this one with line maybe DE.
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You can also say BE; it doesn't matter; DE; any two points on the line.
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DE; those are two intersecting lines; I can also say line P with line L.
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Classify each angle and name the relationship between the two.
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This angle; classify, remember there is three types of angles.
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The acute angle, a right angle, and obtuse angle; this is less than 90.
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I know that because a 90 degree angle is a right angle; that is 90.
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This would be an acute angle.
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This one is greater than 90; it is 135 degrees.
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That is definitely greater; this is an obtuse angle.
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The relationship between these two, I know they are not vertical; they are not adjacent.
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They are probably either going to be complementary or supplementary.
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Let's add these up; this one, 45 degrees plus 135 degrees.
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135 plus 45; 7, 8; they add up to 180 degrees.
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Because they add up to 180, that would make them supplementary angles.
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If they were to add up to 90, then that would be complementary angles.
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The next one, determine the angle relationship between the pair of angles.
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The first is angle 1 or angle 2.
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Again be careful that these are not the angle measures.
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There is no way that this can be 1 degree, 2 degrees.
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These are the names of the angles.
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This angle and this angle here, what is the relationship between them?
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They are next to each other; they share the same vertex and a side.
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These are adjacent; adjacent angles.
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The next one, angle 3 and angle 4, see how they are opposite angles.
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They are formed by intersecting lines; these are vertical; vertical angles.
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The fourth example, name the measure of angle 1; here we have a right angle.
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This angle along with this angle together form that right angle.
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I want to find the angle of this measure right here.
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I know this whole thing is 90.
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If I take 90 and I subtract the 50, don't I get measure of angle 1?
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I can say the measure of angle 1... a shortcut for me to say that is measure of angle 1.
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You know angle 1 is like that.
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But when I am talking about the angle measure, the degrees, then I could put M for measure.
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This just says measure of angle 1; I am talking about the number of degrees.
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Measure of angle 1 plus... this is 50 degrees.
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Together, if I add them together, it becomes 90 degrees.
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How do I solve for measure of angle 1?--I can subtract 50.
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That way measure of angle 1 is 40 degrees.
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This is 40; this is 50; together they add up to 90.
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We know that these two angles are adjacent because they are next to each other.
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They share the same vertex and a side.
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They are also complementary because they add up to 90.
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This angle with this angle together are complementary angles.
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Here straight line.
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That means together measure of angle 1 plus 83 degrees has to add up to 180 degrees.
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Straight line is always 180.
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Again I am going to put measure of angle 1 plus...
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This angle plus this angle, 83 degrees, equals a total of 180 degrees.
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I am going to subtract the 83 degrees.
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Measure of angle 1 is... this is 97 degrees.
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Here these two we know are supplementary because they add up to 180.
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90 so they are complementary; 180 so they are supplementary.
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These are also adjacent angles; they are next to each other; same vertex, side; adjacent.
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That is it for this lesson; thank you for watching Educator.com.