Getting RIGHT with TRIANGLES

Last week, we got more into our study of right triangles. We learned that the Pythagorean Theorem is used to find the missing length of a side of a right triangle. If you have to find the length of one of the legs, you have to turn the Pythagorean Theorem into a subtraction problem, but if you are finding the length of the hypotenuse, you use the Theorem in its original form. Remember to take the square root of the sum or difference! If the radical is not a perfect square, you must attempt to simplify it! We have been using our "bullets" (2, 3, 5, 6, 7, and 10) for some time now, but we have also introduced our "small squares" (4, 9, 16, and 25) in our attempts to simplify the radicals we have been coming up with. You use the small squares after you have gone through all the bullets. Remember also, that when you are simplifying radicals, your goal is to pull the greatest perfect square out of the radical you are simplifying, take the square root of that perfect square, and express your answer as a multiplication problem of the square root and the bullet you used (now expressed as a radical). For example, the "square root of 75" is not a perfect square, so it must be simplified. 75 is the product of 25 x 3, so you would change the radical to "the square root of 25 x 3". Then you give each factor its own radical, and the problem becomes "the square root of 25 times the square root of 3". Then you take the square root of 25 (when you use it, you lose it!), and your answer (the simplified form) is "5 times the square root of 3".

In addition to all that, we reviewed the concept that the interior angles of any triangle always add up to 180 degrees. This is important because if the measure of any of the angles is missing, you can find what it is by simply adding the other two angles and then subtracting the sum from 180. In the case of right triangles, it's even simpler! Since a right triangle has one 90 degree angle, the other two angles have to add up to 90. So to find the missing angle in a RIGHT triangle, you just take the measure of the acute angle that you see and subtract it from 90, and that will give you your missing measure! (See how much stuff we did last week?)

The week culminated with a test, and I must say that we as a team did not do as well as I would have liked, so we will be working more on these concepts on Monday, and for those who wish to do so, I will have a retest on Tuesday. THEN we will begin one of my FAVORITE projects in the 8th Grade curriculum, the THEODORUS WHEEL! Wait until you see it (and create one of your own!)! It is SO cool, and it will help you understand the concept of irrational numbers even better than you do now. So, until next week, see you in the Red Hallway, Knights! 801, SECOND TO NONE!!!