INPUT ARTICLE: Article: The side lengths of a Pythagorean triple are integers that fit the Pythagorean Theorem. These special triangles appear frequently in geometry text books and on standardized tests like the SAT and the GRE.  If you memorize the first 2 Pythagorean triples, in particular, you can save yourself a lot of time on these tests because you can immediately know the hypotenuse of one of these triangles just by looking at the side lengths!   The first Pythagorean triple is 3-4-5 (32 + 42 = 52, 9 + 16 = 25).  When you see a right triangle with legs of length 3 and 4, you can instantly be certain that the hypotenuse will be 5 without having to do any calculations. The ratio of a Pythagorean triple holds true even when the sides are multiplied by another number.  For example a right triangle with legs of length 6 and 8 will have a hypotenuse of 10 (62 + 82 = 102, 36 + 64 = 100).  The same holds true for 9-12-15, and even 1.5-2-2.5.  Try the math and see for yourself! The second Pythagorean triple that commonly appears on tests is 5-12-13 (52 + 122 = 132, 25 + 144 = 169).  Also be on the lookout for multiples like 10-24-26 and 2.5-6-6.5. A 45-45-90 right triangle has angles of 45, 45, and 90 degrees, and is also called an Isosceles Right Triangle.  It occurs frequently on standardized tests, and is a very easy triangle to solve.  The ratio between the sides of this triangle is 1:1:Sqrt(2), which means that the length of the legs are equal, and the length of the hypotenuse is simply the leg length multiplied by the square root of two.  To calculate the hypotenuse of this triangle based on the length of one of the legs, simply multiply the leg length by Sqrt(2). Knowing this ratio comes in especially handy when your test or homework question gives you the side lengths in terms of variables instead of integers. This triangle has angle measurements of 30, 60, and 90 degrees, and occurs when you cut an equilateral triangle in half.  The sides of the 30-60-90 right triangle always maintain the ratio 1:Sqrt(3):2, or x:Sqrt(3)x:2x.  If you are given the length of one leg of 30-60-90 right triangle and are asked to find the hypotenuse, it is very easy to do:  If you are given the length of the shortest leg (opposite the 30-degree angle,) simply multiply the leg length by 2 to find the length of the hypotenuse.  For instance, if the length of the shortest leg is 4, you know that the hypotenuse length must be 8. If you are given the length of the longer leg (opposite the 60-degree angle,) multiply that length by 2/Sqrt(3) to find the length of the hypotenuse.  For instance, if the length of the longer leg is 4, you know that the hypotenuse length must be 4.62.

SUMMARY: Learn to recognize Pythagorean Triple Triangles. Memorize the side ratios of a 45-45-90 right triangle. Learn the side ratios of a 30-60-90 right triangle.

In one sentence, describe what the following article is about: Some people have reported longer hair after reducing the amount they wash with shampoo and conditioner. Consider washing your hair every 2-3 days. On no-wash days, wear a shower cap when you shower and use dry shampoo to help keep oil controlled. If your hair tangles easily, you may need to wash more frequently. Using conditioner daily or every other day can help keep away tangles that may otherwise cause breakage. Damage often starts at the ends of your hair and moves upward toward the roots. Getting regular trims stops damage in its tracks, preserving your locks for the long-haul. See your stylist every 2-3 months and ask them to cut off no more than 0.5 in (13 mm) from your ends to keep the damage from spreading.  If your hair gets damaged unexpectedly by an accident with a hot tool or a chemical treatment, see your stylist as soon as possible. If you don’t have the time or the money for regular salon appointments, you can also try to trim your hair yourself. Try to get a good pair of hair shears if you choose to do this. They make a huge difference. Deep conditioning treatments can help protect your strands and keep tangles away. Look for a hair mask that is formulated for your hair type (e.g., thick, thin, curly, dry, color-treated, etc.). Ask your stylist for help picking the right product for you if you are unsure what will work for you.  Apply the mask to your hair after you shampoo, and leave it on for the amount of time recommended on the packaging. Some masks may take 3-5 minutes, while others may take 10-15. Then, rinse your mask out in the shower. You can find hair masks at most cosmetics and beauty supplies stores, as well as at many pharmacies and drug stores. Brushing can encourage breakage and pull on healthy hairs, so reduce the amount you brush as much as possible. Try to brush only to get tangles out after showers or when styling your hair. When you do brush your hair, make sure to use the right brush. A wide-toothed comb or shower comb works well on both wet and dry hair to remove tangles without pulling too much. Boar-bristle brushes also work well, but are best suited for dry hair. Heat damages your locks from cuticle to tip. That’s why it’s best to stay away from hot tools as much as possible. This includes blow dryers, flat irons, curling irons, hot brushes, crimpers, and hot rollers.  If you must blow dry your hair, use the low setting and stick to your ends. Use a thermal spray if you absolutely must use a hot tool on your hair. Hold the spray arms-distance away from your head and mist your hair before using the hot tool. Certain materials such as terry cloth can be damaging to wet hair. Avoid using terry cloth towels to dry your hair. Instead, allow it to air dry as often as you can. If you need to soak up extra water out of the shower, try using a microfiber towel. Never wrap it and leave it on top of your head. Instead, lightly squeeze out the excess water. Treatments such as coloring, highlighting, perming, chemically straightening, and lightening your hair all cause damage. If you want to grow long, luscious locks, you will need to cut all of these out of your routine. If you already have colored or chemically treated hair, talk to your stylist about how to best transition your style. Many hairdos and styles are hard on your scalps and strands. Styles that pull your hair tight, like high or slick ponytails and certain types of braids, encourage breakage. Avoid damage by wearing your hair down or in loose styles like low ponytails and messy buns as much as possible. Extensions may look pretty at the moment, but your hair may be worse off when you take them out. Try to avoid these styles whenever possible, or use clip in hair extensions to reduce the chances that they will damage your hair.
Summary: Wash your hair 3-4 times a week. Get a trim every 8-12 weeks. Use a weekly deep conditioning mask for a dose of hydration. Minimize the amount you brush your hair. Limit your use of hot styling tools. Avoid terry cloth and use a microfiber towel on wet hair. Skip harsh chemical treatments to prevent damage. Opt for loose hairstyles like low ponytails or messy buns.

INPUT ARTICLE: Article: NutriSystem does not limit the amount of carbs that you can eat. You are simply expected to eat mostly low-GI carbs. Atkins, on the other hand, restricts the quantity of carbs that you can consume. Both diets will require you to change your eating habits for life, but Atkins will require you to more strictly restrict your carb intake. NutriSystem provides you with prepared meals, while Atkins will require you to plan your own menus and cook your own meals.

SUMMARY:
Compare each diet’s philosophy about carbohydrates. Decide which foods you would rather eat. Decide how much you want to cook.