<p>Hey guys, for anyone looking for free help with SAT triangle questions: </p>
<p>I'll post up a triangle question and give you some time to post up your solutions. If you get a question wrong, I'll respond with a short lecture and give practice questions so you can brush up on those question types before I post my solution up.</p>
<p>If this thread goes well, I'll continue going through different math sections one by one (ie, probability, fictional algebra, etc.) based off of your suggestions.</p>
<p>^careful with the direction of the inequality sign
2 < C < 12</p>
<p>Here’s a slightly tricker one that I just made up, but isn’t much harder: In quadrilateral ABCD, AB = 5, BC = CD = 6, DA = 8. What are all possible lengths of BD?</p>
<p>For the problem posted by @MiTer94 ,
3 < BD < 12. We can split the problem into two triangles: AB, BD, and DA; and BC, CD, and BD. For the first triangle, 3 < BD < 13, and for the second triangle, 0 < BD < 12 (in both cases I am using the triangle inequality). For the two triangles to fit together into a quadrilateral, BD must be a possible diagonal, so it has to fit the requirements to be the third side of both triangles, meaning 3 < BD < 12.</p>
<p>The highest or lowest number for a side is less than the added total of the other two sides or the subtraction of them. So it can be greater than 2 but less than 12</p>
<p>This type of threads should be more helpful to students if it related to actual questions. I understand that some might be cautious with QAS or similarly recent tests, but questions that have appeared in the Blue Book have been addressed multiple times. </p>
<p>With all due respect to their authors, what I call synthetic questions (written by non ETS people) are prone to irrelevance and misleading answers. With the huge library of official questions that have been available, it is silly to waste time on amateurish questions, and this no matter how noble the attempt is. </p>
<p>With that being said, the goal for this thread is to help students who have issues with understanding certain triangle properties to improve their scores. Triangle concepts can get confusing and I’m just here to help anyone with triangle concepts they want to understand better.</p>
<p>^There have been many “official” questions regarding triangle properties. Given the study you cite above and your comments in that same paragraph, wouldn’t it make more sense to learn triangle properties through College Board questions?</p>
<p>X= 105. By noticing the sides opposite the angles not given are the same marks the triangle as isosceles. So since the interior angles add up to 180. 180-30(given angle)=150, which then can be divided by 2 to find the other 2 angles, which must be the same due to it being isosceles. Then the angle near x plus x should equal 180. So x=180-75 x=105</p>
<p>Hey @CHD2013
You’re right, that does sound contradictory. </p>
<p>Context is important, so heres the context of the study.</p>
<p>So basically, with students, theres two categories:</p>
<ol>
<li><p>People who have some base level understanding
For this group, they should work with the blue book and college board questions at checkpoints to monitor progress. If they run out of questions to practice they can supplement practice with questions based off college board questions. (ie. using the same college board question format and switching the numbers.) So the study applies to people with some level of understanding.</p></li>
<li><p>People who don’t understand concepts.
For these students, simply practicing questions is not helpful. If anything it can be a frustrating experience. It’s important to isolate each knowledge gap and fix each gap one by one with explanations. </p></li>
</ol>
<p>This thread is using this methodology.</p>
<ol>
<li>Posting questions to diagnose knowledge gaps</li>
<li>Analyzing specific weaknesses.</li>
<li>Addressing weaknesses with discussion and activities.</li>
<li>Repetition (Turning knowledge into an actionable skill. This is where the college board questions are great.)</li>
<li>Monitor Progress with Tests that Simulate Real Situations (This is where college board questions are great.)</li>
</ol>
<p>This is the same methodology used by Philharmonic Orchestras, Olympic Coaches, and most people who achieve in the top 5% of a skill category. You can read more about this, written by our colleague at this link. <a href=“A Better Way to Practice”>A Better Way to Practice; </p>