PA ch 12 01 Parallel Lines and Transversals Lesson Video

hello welcome everyone today we're gonna be talking about parallel lines and this thing called transversals so real quick review on parallel and perpendicular lines so parallel lines or parallel lines we indicate the parallel lines by having these little arrows going in the same direction so we say and are parallel we also have an indication for what perpendicular lines are so perpendicular lines make 90-degree angle and that's what this box is here so we could say lines and are perpendicular so we're gonna use this information as we're moving through our lesson today so our next vocab word is called transversal so transversal so transversal is line that intersects two or more lines now we have special case our special case is when parallel lines are cut by transversal we make several congruent angles and the angles that are congruent are the corresponding angles so the colored arcs indicate the corresponding angles and each of these corresponding angles is congruent so we have the purple single arc so these two angles are congruent because we have two parallel lines and being cut by transversal well we do that we create these congruent corresponding angles so have the two purple ones are congruent the two blue ones are congruent the two green corresponding angles are congruent and the corresponding red our angles are congruent okay now we also know few things about these that our purple and blue angles here those are vertical angles which means these are also congruent and if these are congruent then these are congruent similarly the green and the red are vertical angles so those are all congruent so really in the end we just have two different angles we have an acute angle and obtuse angle all the acute angles are going to be congruent all of the obtuse angles are going to be congruent all right so let's go ahead and carry on here so let's use that information to find some missing measures so use the figure to find the measures of angle one and two actually let's use it to find the measures of all of these angles that are identified here so first off let's look at example hundred and ten degrees is this angle here so the corresponding angle and again we have two parallel lines and cut by transversal we know that the hundred and ten degree angle corresponds with angle number one so we know that both of those angles are hundred and ten degrees so you could say that measure of angle 1 is equal to 110 degrees well what do we know about angle to you well angle two is adjacent and on the same line here so that means we have supplementary angle so measure of angle two is supplementary to measure of angle one so to find that we subtract the measure of angle one from 110 and the measure of angle two is going to be equal to 70 degrees all right so let's go ahead and look at example so example we have lot of different options to find the missing angles so let's go ahead and look at angle one here so angle one angle one is on the same line as the 59 degree angle so that means measure of angle 1 is going to be supplementary to 59 degrees so 180 minus 59 is equal to hundred and twenty one degrees so measure of angle one is hundred and twenty-one degrees now what about measure of angle two well that's vertical angle right it's opposite of the 59 degree angle so we know that's 59 degrees and we know angle 1 and angle 3 are vertical angles so that's hundred and twenty one degrees also when you start to see pattern here all right now let's go ahead and find four five six and seven and use our notion of congruent corresponding angles between our parallel lines LNM and our transversal so let's look at four here four is corresponding to one so 4 corresponds to 1 which means angle 4 is 121 degrees now we can go ahead and use corresponding angles or vertical and supplementary angles to find the rest let's just talk about corresponding angles angle 5 corresponds to this 59 degree angle that's 59 degrees angles 3 and 6 correspond to each other others so that's 121 and angles 2 and 7 correspond to each other so they are 59 degrees and notice all of the acute angles are congruent all of the obtuse angles are congruent so what we can do now is we could say that the measure of angle 1 is equal to the measure of angle 3 which is equal to the measure of angle 4 which is equal to the measure of angle 6 which is these are all each 121 degrees only have the measure of angle 2 is equal to the measure of angle 5 and the measure of angle 7 those are all 59 degrees all right to go ahead and head on over to the on your own pause the video give these try alright so for measure of angle one is 63 degrees it corresponds with the 63 degree angle that was given and then at measure of angle 2 is supplementary to angle 1 so that's hundred and seventeen degrees for again we can start off with angles one two and three first angle one is vertical to the given 75 degree angle so that's 75 degrees and angles 2 & 3 are both supplementary to these angles so those are 105 degrees and now we can use on our corresponding angles to find 4 5 6 & 7 4 corresponds to 1 5 corresponds to 2 6 corresponds to the given 75 degree angle and 7 corresponds to angle 3 and we have all of the acute angles are 75 degrees all of the obtuse angles are 105 degrees all right so that's good practice and we should notice something some patterns as we're working with these parallel lines and transversals before we get into any more these problems let's look at some vocabulary so we have different angle types so the interior angles of two parallel lines cut by transversal are called or are on the inside of the parallel lines so we have parallel lines and and we call angles 3 4 5 & 6 we call them in two your angles because later on the inside of the parallel lines so they're in between on the inside of the parallel lines now exterior angles are outside the parallel lines so angles 1 2 7 and 8 are called exterior angles because they're on the outside of the parallel lines okay so we have exterior angles that are outside the parallel lines interior angles on the inside now we can be even little more specific we can actually break down our interior and exterior angles into alternating angles and what we see is that these alternating angles are congruent well we saw this way back in our examples here where our alternating interior angles are congruent and our alternating exterior angles are congruent what we mean by alternating is that we have our transversal here our transversal and they're alternating because they are on the opposite sides of that transversal so the alternate alternate interior angles are the red single arcs and the blue double arcs they are on opposite sides of the transversal and then the exterior ones that alternate again are the blue and red arcs notice they're on the opposite sides of the transversal what we could say is these are congruent and the alternating angles are congruent let's go ahead and use that information to solve some problems here so we have clearance sale sign and all of the letters are at an 80-degree angle so here are two parallel lines at 80 degrees and they are like cut by transversal so this is our transversal here and we want to know what the angle of measure 1 is so we could use our knowledge of alternate interior angles for this one because 80 degrees is going to be congruent to this angle right here which is the alternate interior angle on the inside of the parallel line so we know that this is 80 degrees right here so when our angle 1 is supplementary to 180 so 180 minus 80 so measure of angle 1 is equal to 180 minus 80 because it's supplementary that is hundred degrees so the measure of angle one is hundred degrees now similarly we could have used supplementary angles here and found out that this angle right here was hundred degrees and then use the fact that this hundred degrees and angle one are alternate interior angles to give us hundred degrees all right so let's go ahead and let you practice it on your own go ahead and pause and give it try all right so first talking about relationships angles 3 and 6 here so here's three here's 6 these are on the exterior they're on the outside of the parallel lines so their exterior angles on the opposite side of the transversal so they are alternating exterior angles and then we have two and seven so here's angle - here's angle seven they are on the inside of the parallel lines so their interior angles on the opposite sides of our transversal so alternating interior angles alright so if we know that measure of angle 4 is 84 degrees how can we find the measure of angle three all that is supplementary to angle four so wanna 80-84 is 96 degrees measure of angle five is an alternate interior angle of angle four so we know that's 84 degrees and angle six is an alternate exterior angle of angle three so we know that's 96 degrees and again once we find the acute and obtuse angle we can find the rest of them any acute angle is going to be 84 degrees any of two singles going to be 96 degrees all right well that does it for our lesson on parallel lines and transversals