Explanation for Question 10 From the Math (No Calc) Section on the 2020 October Sat
So question number 10 gives us a triangle ABC and asks us where we 2 should put point F if we want it to be similar to triangle or 3 triangle D F E to be similar to triangle ABC. 4 And so the first thing that we need to know is that similar triangles 5 have the same angle measures, but their sidelights are different, 6 but they're not different in any random pattern, 7 right? There are some they're different by being multiplied by a constant number. 8 So the side links could be doubled the size. 9 They could be triple the size, but all the sidelights will be multiplied by 10 the same factor. So the first thing will be useful to do is decide 11 which side links correspond with which side links. 12 And we see that a B is the first length on this triangle. 13 We see that here. So that means that D F will be the corresponding 14 one. 15 And we don't quite know where that one is yet, but we do know 16 that BC is this one and F E goes 17 here. And so the length of a, 18 to C is going to be similar to the length of the 19 T E. So it goes here and by now 20 we can see that there's been a little bit of manipulation happening because here 21 the line goes up and here the line goes down so we can see 22 there's kind of been a mirroring as well. 23 We go in opposite directions. And the first thing will be useful to do 24 is to see how far away a and C are from each other. 25 Now in this triangle, we see that we go over three and up one 26 to get to see, however, 27 the distance in this t...