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Hey cats, first post here on SDN. So I took the DAT yesterday. My AA was 24 and PAT was 26, i'm pretty happy about that. I've found SDN helpful for answering my questions and wanted to give back to the community or something like that.
My scores in the PAT gradually improved in all areas overtime but angles were consistently low. I tried laptop/hill/quickglance but none of those did it for me, so I came up with a few of my own that helped take the guess work out of angle ranking. Maybe some of these are already in the community, I dont know, but these were the best for me presented in order of most helpful:
[Note: only use these techniques if you can't tell the difference by inspection. If you can already tell which one is smaller, it would be silly to do anything else.]
1. Parallel lines
This only works when you have parallel lines in the problem, so you might get 3 or 4 that this helps on, but it may reduce the answers down or in rare cases solve the problem.
This one is pretty easy to figure out. A and C are clearly smaller than B and D. Because the horizontal base is the same, you can ignore it in your deduction, only focue on the diagonal lines because those are the only difference. Ask yourself "Where do these lines intersect?" Extrapolate the diagonals in A and C and follow them. Do they intersect above or below? They cannot intersect above so they must intersect below leading us to conclude A is smaller than C.
Here is another with obtuse angles. The smallest is clearly B. From there we use the diagonals of A C and D to solve. Extrapolate A C and D. Just at a glance, we see the diagonal line in A will intersect with the diagonal lines C and D, so A is the next smallest. D will clearly intersect with C so C is the next smallest. Note that C being elevated does not affect our reasoning in this problem.
These use to make me cringe... until I saw it. Lets look at A and B. Once again because the lines are parallel we can ignore them and only focus on the diagonals of A and B. Where do they intersect? They clearly point below, leading us to the fact A is smaller than B. Focus next on B and C. Follow the diagonals, they intersect above, so C is smaller than B. Following the diagonals in A and C we see they would intersect above so C is smaller than A. C and D are last. Following the diagonal in D we see clear as day that it intersects above the parallel lines.
If it doesn't make sense, try playing with one of the angles in your mind. make it and smaller. For acute angles, if you swing it shut and the intersect doesn't switch sides in the process then it is smaller.
Like I said, this technique wont work for every problem, and usually wont solve the problem but it will narrow down the answers in some cases and take some of the guess work out. It feels good to know.
2. Reference angles.
I dont know why the human mind diserns when something is less than or greater than 90 but it does. The reference angles you want to be familiar with are 45, 90 and 120.
Here is an easy one. A is 90. B is <90 and. C and D are both >90. Using parallel lines, we can tell C and D intersect below so C is smaller than D.
Now here is the meat and more likely to show up on your DAT. Looking at A we can tell its <90. B is >90. C is <90 and D appears to be just on the mark of 90. So its down to A and C. You can tell C is only off by a little and A is off of 90 by more than that so A must be the smallest.
90 degrees is the easiest to work with. 45 is a little more tough.
On inspection you can probably tell C is the smallest and B is the largest but then its A and D. Using the reference angle of 45 degrees will be helpful. You will have to tilt your head to get one of the lines horizontal with your vision. If we look at D we can tell it is smaller than 45 degrees. Tilting our head to A we can see it is right around 45. This may take a bit of practice and you may look a bit silly trying to turn your head around these angles, but it works for a lot of them. Also, this method will not work when the angles are all around 70 degrees
This method is less accurate than parallel lines, but it will come up more frequently than the others and mastering it will reduce your angles problems like LAH reduces a carboxylic acid.
3. Quick draw method
My last resort was a method I like to call the quickdraw method. It is the least accurate but still has value. I developed this because i noticed that when i went through the angles I got wrong I could clearly tell one was smaller (by inspection) and wondered how I could have missed such an obvious cue. After 5 minutes of angles they all start to blend so you have to clear your mind.
When you've narrowed it down to two angles, get the numbers in your mind and repeat them over so you remember them. Press the "Previous" button at the bottom the the test to go back to the previous problem (bear with me here). Clear your mind of all things angle related at this point. Read something on the screen like the "MARK' button or "Time remaining". Then quickly press the "Next" button to go back to your problem and look at the two angles in question. Go with your gut, usually, one of them stands out. If one doesn't, mark it and move on, then come back after shape folding. Your mind will be totally clear from angles at that point and one should clearly stand out. Yesterday after shape folding I came back to one I had marked and the difference was so obvious I almost kicked myself for having such a hard time deciding. I quickly changed it to the right answer.
Wow that was long, Hope it helps. I also reccomend doing a few CDP "random test" with angles if they are still your weak point. Good luck!🙂
My scores in the PAT gradually improved in all areas overtime but angles were consistently low. I tried laptop/hill/quickglance but none of those did it for me, so I came up with a few of my own that helped take the guess work out of angle ranking. Maybe some of these are already in the community, I dont know, but these were the best for me presented in order of most helpful:
[Note: only use these techniques if you can't tell the difference by inspection. If you can already tell which one is smaller, it would be silly to do anything else.]
1. Parallel lines
This only works when you have parallel lines in the problem, so you might get 3 or 4 that this helps on, but it may reduce the answers down or in rare cases solve the problem.
This one is pretty easy to figure out. A and C are clearly smaller than B and D. Because the horizontal base is the same, you can ignore it in your deduction, only focue on the diagonal lines because those are the only difference. Ask yourself "Where do these lines intersect?" Extrapolate the diagonals in A and C and follow them. Do they intersect above or below? They cannot intersect above so they must intersect below leading us to conclude A is smaller than C.
Here is another with obtuse angles. The smallest is clearly B. From there we use the diagonals of A C and D to solve. Extrapolate A C and D. Just at a glance, we see the diagonal line in A will intersect with the diagonal lines C and D, so A is the next smallest. D will clearly intersect with C so C is the next smallest. Note that C being elevated does not affect our reasoning in this problem.
These use to make me cringe... until I saw it. Lets look at A and B. Once again because the lines are parallel we can ignore them and only focus on the diagonals of A and B. Where do they intersect? They clearly point below, leading us to the fact A is smaller than B. Focus next on B and C. Follow the diagonals, they intersect above, so C is smaller than B. Following the diagonals in A and C we see they would intersect above so C is smaller than A. C and D are last. Following the diagonal in D we see clear as day that it intersects above the parallel lines.
If it doesn't make sense, try playing with one of the angles in your mind. make it and smaller. For acute angles, if you swing it shut and the intersect doesn't switch sides in the process then it is smaller.
Like I said, this technique wont work for every problem, and usually wont solve the problem but it will narrow down the answers in some cases and take some of the guess work out. It feels good to know.
2. Reference angles.
I dont know why the human mind diserns when something is less than or greater than 90 but it does. The reference angles you want to be familiar with are 45, 90 and 120.
Here is an easy one. A is 90. B is <90 and. C and D are both >90. Using parallel lines, we can tell C and D intersect below so C is smaller than D.
Now here is the meat and more likely to show up on your DAT. Looking at A we can tell its <90. B is >90. C is <90 and D appears to be just on the mark of 90. So its down to A and C. You can tell C is only off by a little and A is off of 90 by more than that so A must be the smallest.
90 degrees is the easiest to work with. 45 is a little more tough.
On inspection you can probably tell C is the smallest and B is the largest but then its A and D. Using the reference angle of 45 degrees will be helpful. You will have to tilt your head to get one of the lines horizontal with your vision. If we look at D we can tell it is smaller than 45 degrees. Tilting our head to A we can see it is right around 45. This may take a bit of practice and you may look a bit silly trying to turn your head around these angles, but it works for a lot of them. Also, this method will not work when the angles are all around 70 degrees
This method is less accurate than parallel lines, but it will come up more frequently than the others and mastering it will reduce your angles problems like LAH reduces a carboxylic acid.
3. Quick draw method
My last resort was a method I like to call the quickdraw method. It is the least accurate but still has value. I developed this because i noticed that when i went through the angles I got wrong I could clearly tell one was smaller (by inspection) and wondered how I could have missed such an obvious cue. After 5 minutes of angles they all start to blend so you have to clear your mind.
When you've narrowed it down to two angles, get the numbers in your mind and repeat them over so you remember them. Press the "Previous" button at the bottom the the test to go back to the previous problem (bear with me here). Clear your mind of all things angle related at this point. Read something on the screen like the "MARK' button or "Time remaining". Then quickly press the "Next" button to go back to your problem and look at the two angles in question. Go with your gut, usually, one of them stands out. If one doesn't, mark it and move on, then come back after shape folding. Your mind will be totally clear from angles at that point and one should clearly stand out. Yesterday after shape folding I came back to one I had marked and the difference was so obvious I almost kicked myself for having such a hard time deciding. I quickly changed it to the right answer.
Wow that was long, Hope it helps. I also reccomend doing a few CDP "random test" with angles if they are still your weak point. Good luck!🙂
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