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In the diagram below, quadrilateral EFGH-- so that's this one here-- was obtained by performing a sequence of transformations on quadrilateral ABCD. And then they tell us the information that's already written here. Measure of angle A is 69 degrees. Measure of angle B is 102 degrees. Measure of angle G is 145 degrees. And measure of angle H is 44 degrees. Which of the following additional facts is sufficient to conclude that the only transformations used were translations, rotations, reflections, and dilations, and not any other kind of transformations? So this is another way of saying, if we only used translations, rotations, reflections, and dilations, then that means that these two figures are similar. So if this is the case, then we're dealing with similar quadrilaterals. So another way of saying this is, which of these facts-- so either this first fact, or this second fact, or both of them, or neither of them-- which of these facts are sufficient in order to determine that these two quadrilaterals are similar, which is another way of saying that you could go from one to another only through translations, rotations, reflections, and dilations? So let's look at this first set of facts right over here. So they give us the measure of angle C is 145 degrees. So they tell us that right over there is 145 degrees. And they tell us that the measure of angle E is 69 degrees. So they tell us that this is 69 degrees. So with that piece of information right over here, in each of these quadrilaterals, we know three of the angles. And because we know three, we can figure out the fourth. We can figure it out because the sum of the angles in a quadrilateral are going to add up to 360 degrees. So if we wanted to figure out the measure of angle F right over here-- let's say that is x-- we could say that x plus 69 degrees plus 145 degrees plus 44 degrees is equal to 360 degrees. So let's get the calculator out right over here. Our x would essentially be 360 minus these things. So 360 minus 69 minus 145 minus 44 is 102 degrees. So this angle right over here is 102 degrees. Now notice, these two already have three angles in common. They have a 69 degree-- let me color code it-- so this angle right over here has a measure of 69 degrees. So does this one. Then you move one over. This angle right over here is 102 degrees, so is this one. Then you move to the next angle is 145 degrees, well, that would correspond to this one. And if you know three of the angles, you know that this last one right over here, this fourth one, was going to have to be 44 degrees. You could take 360 and from it subtract 145, 102, and 69, and you will get 44 degrees. So you have two quadrilaterals where all of these angles are congruent to each other. So if you have these two shapes and you have all the corresponding angles are congruent to each other, then you know that they are similar. And if you know that they are similar, you know that you can go from one to another purely through some combination of translations, which is really just shifting it in two dimensions, rotating it around some points, reflecting it, which you can kind of use flipping it over around some line, and dilations, which is scaling it up or down. So the first one is definitely good. Let's see if the second one could also independently help us determine that these two things are similar. So what I'm going to do is clear this out so I have some space to work with. Let me clear it out. Let me clear this right over here. And now let's think about what the second statement is telling us. The second statement tells us the measure of angle D is 44 degrees. So they're saying that is 44 degrees. And that the measure of angle F is 102 degrees. So once again, it's given us one more angle in each of them. And from that, we can figure out the last angle. And so if you know all of the angles in two quadrilaterals, you can determine if they are similar. They're going to be similar only if you have four corresponding angles that are congruent to each other. Let me just show it to you just so I don't say that it's enough. Let's calculate this last angle right over here. We can get our calculator back out. It's going to be 360 minus 102 minus 145 minus 44, which is equal to 69 degrees. So this right over here is 69 degrees. So notice, 102 degrees, then 69 degrees, then 44 degrees. And so this last one has to be 145 degrees, just like this one. If three of the angles are the same, that fourth one has to be the same. So this angle corresponds to this angle. This angle corresponds to that angle. This angle corresponds to that angle. And then finally, this angle corresponds to this angle. You have two quadrilaterals. The interior four angles are all congruent. They correspond to each other. So they must be similar. And so you can get from one to another through translations, rotations, reflections, and dilations. So this one is also good. So actually, either of these are sufficient in order to conclude that the only transformations used were these. So I would click, both answers are correct.