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# Хувиргалтын дараалал

## Video transcript

in past videos we thought about whether segment lengths or angle measures are preserved with a transformation what we're now going to think about is what it's preserved with a sequence of transformations and in particular we're gonna think about angle measure angle measure and segment lengths so if you're transforming some type of a shape segment segment lengths so let's look at this first example they say a sequence of transformations is described below so we first do a translation then we do a reflection over a horizontal line PQ then we do a vertical stretch about PQ what is this going to do is this going to preserve angle measures and is this going to preserve segment lengths well a translation is a rigid transformation and so that will preserve both angle measures and segment lengths so after that angle measures and segment lengths are still going to be the same a reflection over a horizontal line PQ well a reflection is also a rigid transformation and so we will continue to preserve angle measure and segment lengths then they say a vertical stretch about PQ well let's just think about what a vertical stretch does so if I have some triangle right over here if I have some triangle that looks like this that stays triangle a b c and if you were to do a vertical stretch what's going to happen well let's just imagine that we take these sides and we stretch them out so that we now have a is over here or a prime i should say is over there let's say that b prime is now over here is this is going to be exact well what just happened to my triangle well the measure of angle c is for sure going to be different now and my segment lengths are for sure are going to be different now a prime c prime is going to be different than a c in terms of segment length so a vertical stretch if we're talking about a stretch in general this is going to preserve neither so neither preserve served neither preserved so in general if you're doing rigid transformation after rigid transformation you're gonna preserve both angles and segment lengths but if you throw a stretch in there then all bets are off you're not going to preserve either of them let's do another example a sequence of transformations is described below and so they give three transformations so pause this video and think about whether angle measures segment lengths or well well either both or neither or only one of them be preserved all right so first we have a rotation about a point P that's a rigid transformation it would preserve both segment lengths and angle measures then you have a translation which is also a rigid transformation and so that would preserve both again then we have a rotation about point P so once again another rigid transformation so in this situation everything is going to be preserved so both angle measure angle measure and segment length are going to be preserved in this example let's do one more example so here once again we have a sequence of transformations and so pause this video again and see if you can figure out whether angle measures segment lengths both or neither are going to be preserved so the first transformation is a dilation so a dilation is a non rigid transformation so segment lengths not preserved segment lengths not preserved and we've seen this in multiple videos already but in a dilation angles are preserved angles preserved so already we've lost our segment lengths but we still got our angles then we have a rotation about another point Q so this is a rigid transformation it would preserve both what we've already lost our segment lengths but angles are going to continue to be preserved and then finally a reflection which is still a rigid transformation and it would preserve both but once again our segment lengths got lost through the dilation we will preserve continue to preserve the angles so in this series of after these three transformations the only thing that's going to be preserved are going to be your angles