Explanation for Question 17 From the Math (No Calc) Section on the Official Sat Practice Test 1
So looking at question number 17, we can see that they're asking us to 2 solve for X, which is this length right here. 3 And now, if we look at our question, it tells us that a B, 4 so this length is 1800 E B is going to be 1400, 5 which we can see right here. B D is going to be B D 6 the third one. So 700. And then finally a CD is the 7 last one, 800. And so they've given us all of these side links, 8 and then they want to know what X is, right? So we're solving for 9 this length here, but they also tell us something about the angles. 10 First, they tell us that this angle in the single are congruent, 11 but we can also see that these two angles have to be congruent as 12 well because they're vertical angles. They come from an intersection and the two angles 13 opposite intersection are always congruent. 14 And so the fact that we have two angles congruent means that our third 15 one also has to be the same. And if we have three, 16 uh, angles of the same measure in two different triangles and all the 17 angles are the same, that means that the triangles are similar. 18 And so their, their size will occur at a perfect ratio. 19 Now, if we look at this side, right, if we look at the 700 20 over this side, it's, 21 um, I guess the version of that side on the bigger triangles, 22 1400, right? So what we've done is we've taken that side on the little 23 triangle and we've multiplied it by two. And so now the side that corresponds 24 to X is going to be the 800, 25 right? And so if I'm just taking the little side triangle they'll triangle, 26 or the side on the little triangle, and I multiply it by two to 27 get to my big triangle, but I can take this 800 and multiply it 28 by two to get the side on the big triangle. 29 And 800 times two is 1600. So X is going to be equal to 30 1600.