lesson 8.2 b two angles and their included side so before we start for a quick review this is a protractor it's a tool for measuring angles this is a compass it's a tool for drawing circles and arcs a unique triangle is formed when the sum of the measures of the two shorter sides is greater than the measure of the third side so if we had these line segments a b and c and this was three inches this was four inches and this was five inches we could say a plus b is greater than c these measures will make a unique triangle as a closed figure because these two three plus four is seven that is greater than five if the sum of the two shorter measures is less than or equal to the measure of the third side no triangle can be formed if a plus b is less than or equal to c that means no triangle is formed an included side is a side of a polygon between two given angles here we have a b and c so this is angle a this is angle c this angle right here and this angle right here is angle a segment ac that's in between this angle and this angle so it's segment ac is the included side between angle a and angle c a protractor has degree measures on the outside and the inside of its curve there's a hole in the center of the straight part that is used to line up the vertex of an angle so that where this hole is right here that's where the vertex would be see and we would line the hole up on the vertex and then we would put this line lined up on our base and we can measure the angle this is a 120 degree angle we would use the inside scale here see how there's a 60 up here but there's a 120 here because this angle is facing right we're going to use the inside scale now this scale is opening this way it's facing left so we're going to use the outside so that is a 120 degree angle using the outside scale we can use a ruler and a protractor to draw triangles with two given angle measures and an included side with a given length so it's telling us the angles need to be 40 degrees and 60 degrees and the included side length is 5 inches so we take a ruler we draw a 5 inch line segment like that so that's going to be the base then we take our protractor and we measure a 40 degree angle we put this right here we put the circle right there on the vertex and where the 40 degree mark is we put a little mark so that we can line it up and use the straight side to make our ray we do the same thing for this side so when we did this one we used the inside measures okay we're using the inside measure of the curve here now we're going to use the outside measure because it's facing left the opening so we'll come here and we can put a little mark showing where the 60 degrees is then we use the straight side to draw our ray like that and we have an angle included side and angle angle side angle see that so we just made our first triangle with a five inch included side we have a 40 degree angle a 5 inch included side and a 60 degree angle that's our triangle we can make a second triangle we can make a triangle with angles 50 degrees and 70 degrees with an included side that is three inches long we draw a three inch side and we take our protractor and using the inside measures the inside measures right here and we find out where 50 degrees is lining up our circle and the straight line at the bottom and we mark that 50 degrees we can put a little mark there and then we use the straight side to make our ray then we measure mark and draw a 70 degree angle so now we're going to be using the outside measures along here because it's opening to the left so we line this up with the circle and with the straight line we can put a mark where 70 degrees hits right here and we use the straight side to draw the ray and when we are given two angle measures and given the length of an included side we get a unique triangle so this is a unique triangle and this is a unique triangle it has this included side is 5 inches this included side is 3 inches this one has a 40 degree angle and 60 degree angle this one has a 50 and 70. they're unique to each other aren't they they have different side length they have different angle measures we've made unique triangles when we measure mark and draw an angle we can draw the line with an arrowhead to show it continues in that direction and we can see that the orange ray will continue eventually intersecting this green one won't it it'll eventually intersect it and it'll form a unique triangle here we can see that the orange ray will not intersect the green ray a triangle will not be formed there's no triangle they'll continue on in those directions we won't have a triangle now take a look at this one we have an 80 degree angle and this ray is continuing up in this direction with the arrow but this is just a two inch segment and we have a three and five tenths inch base here well since the orange segment only has a 2 inch length it will never intersect with the green ray of the 80 degree angle it stops right there there's no arrow head that's no triangle here we have the same base of 3 and 5 10 inches now we have a 35 degree angle and we have a 3 inch line segment right here well we can see the green ray forming the 35 degree angle will continue and then intersect with the orange three inch segment to form a unique triangle if a triangle has the angle measures 30 degrees 60 degrees 90 degrees is it a unique triangle let us find out by drawing it with a four inch base and a six inch base we draw a four inch base we make a 30 degree angle and a 60 degree and a 90 degree angle so that's a that's a square corner isn't it this one is a right angle and that means this is going to be a right angle well if you take a look at them they're just larger or smaller versions of each other since more than one triangle can be drawn with those angle measures and have corresponding sides of different lengths it's not unique this side corresponds to this side this side corresponds to this side the green to the green and the orange corresponds to the orange since more than one triangle can be drawn with those angle measures and have corresponding sides of different lengths it's not unique we're finished with lesson 8.2 we're moving on to 8.3 which is about cross sections 8.3 a is cross sections of a right rectangular prism remember a unique triangle is formed when the sum of the measures of the two shorter sides is greater than the measure of the third side have a wonderful day and join me for the next lesson bye you