![]() ![]() ![]() ![]() So as we flip it over, as weĭo the reflection over DE, the angle will be preserved. Would then be mapped to F? Well, this angle would be preserved due to the rigid transformation. Reflect point C prime over that to get right over there. We can just do a reflection about DE, or A prime B prime, to And in that case, we can just do one more In which case, C prime wouldīe mapped right over there. Of rigid transformations, looks something like this. Possibility that side AC, due to our rigid transformations, or after our first set But there's another possibility that the angle gets conserved, but side AC is mapped down here. Our rigid transformation based on SAS, and so therefore the two triangles would be congruent. Here, and if that's the case then F would be equal to C prime, and we would have found So either side AC will be mapped to this side right over And so we also know thatĪs we do the mapping, the angle will be preserved. We also know that the rigid transformations So C prime is going to be some place, some place along thisĬurve right over here. C prime it's distance is going to stay the same from A prime. Point that C gets mapped to after those first two transformations. Preserve distance, we know that C prime, the And so since all of these rigid transformations The distance between AĪnd C is just like that. Where would C now sit? Well, we can see theĭistance between A and C. Second rigid transformation, point A will now coincide with D. But then we could doĪnother rigid transformation that rotates about point E, or B prime, that rotates that orange side, and the whole triangle with it, onto DE. Transformation to do that, if we just translated like that, then side, woops, then side B A would, that orange side wouldīe something like that. The way that we could do that in this case is we could map point B onto point E. Segment onto the other with a series of rigid transformations. With the same length that they are congruent. That have the same length, like segment AB and segment DE. So the first thing that we could do is we could reference back to where we saw that if we have two segments Transformation definition the two triangles are congruent. That allow us to do it, then by the rigid Because if there is a series of rigid transformations So to be able to prove this, in order to make this deduction, we just have to say that there's always a rigid transformation if we have a side, angle, side in common that will allow us to map Or the short hand is, if we have side, angle, side in common, and the angle is between the two sides, then the two triangles will be congruent. Lengths or measures, then we can deduce that these two triangles must be congruent by the rigid motionĭefinition of congruency. We have a side, an angle, a side, a side, an angle and a side. And the angle that isįormed between those sides, so we have two correspondingĪngles right over here, that they also have the equal measure. Has the same length side as this orange side here. Side has the same length as this blue side here, and this orange side Of corresponding sides that have the same length, for example this blue Two different triangles, and we have two sets Going to do in this video is see that if we have ![]()
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