In one sentence, describe what the following article is about: 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: Make sure that no one is angry or emotional beforehand and that you have plenty of time to talk about any issues. Don't bring this up in front of younger siblings. You might make notes for yourself, so you don't forget to touch on every point. Explain to them exactly why you think you can handle this particular freedom, and don't raise your voice. Becoming angry or upset will only prove to them that you are not yet mature enough to handle additional freedom.  Identify which specific freedoms you want. This might be a later curfew, more computer time, or permission to go to a concert. Be prepared that this might be an ongoing conversation. They may need to think about it before making a decision. Talk through any concerns that they might have. For instance, if you're asking to go out with a friend, see if you can get them in contact with that friend's parents. Remember to remain calm, even if they say things you disagree with. Think about any possible risks or consequences, and be ready to answer any questions your parents might have. Perhaps you get decent grades consistently, do your chores without complaints, and interact well with your siblings. Remind them of how responsible and hardworking you've been acting recently. If you've done anything particularly special, such as cooking dinner for your parents or taking on more chores, be sure to include that as well.
Summary: Choose an appropriate time to discuss this topic. Ask them in a calm and mature manner. Consider their point of view. Give recent examples that prove that you are dependable.

In one sentence, describe what the following article is about: The most important part of the speech isn't the speaking style or the charisma of the speaker, it's the content of what is said. Giving a speech is hard because it has all the challenges of writing an essay, with the added difficulty of having to make it easy to listen to out loud. The most important thing to focus on in your evaluation is the content of the speech. If it's a persuasive speech, or an argument speech, the content will likely include a lot of research, real-world examples, and main points. In an informal speech, the content will likely involve anecdotes, stories, and jokes. When you're evaluating, keep in mind the following questions and answer them as a way of giving feedback:  What was the main argument of the speech? Was the content clear and well-articulated? Was the argument supported with research? Good examples? Was the content made clear to the audience? Did the speaker prove their point? In order to make the content of a speech clear and easy to digest, it needs to be organized well. Formal or informal, public speaking needs to be easy to listen to. If the speech jumps around or moves from point to point like a tennis match, it might need to be reorganized. To help you evaluate the organization of the speech, keep in mind the following questions to generate feedback for the speaker:  Was the supporting argument logically structured? Was the speech easy to follow? Difficult? Why? Do the speaker’s points flow logically from one to the next? What could be included to clear up the speech for you? If the content of the speech refers to what is spoken, the style refers to how it is spoken. A good speech should match the style to the content: it's unlikely a serious paper about dolphin populations would involve "getting to know the audience" games or audience participation. Whether or not a speaker chooses to use jokes, how much the speaker engages with the audience, and other personal elements to the speech will all play into the style. How a speech is written will affect the style, but also how it is performed. Are the jokes told like they are jokes? Is research presented accurately and clearly? Keep in mind the following questions:  How would you describe the style of the speech and the speaker? Did the style of the speech work for the content, or against it? Why? How convincing was the speaker? How was the timing of the speech? Was it easy to follow? The tone of the speech refers to the overall impact of the content and the style. A tone might be light, or serious, or playful, and there's no right or wrong tone for any content. It might be appropriate to tell light stories and jokes at a eulogy, or it might be disastrous. It might be appropriate to tell a heartwarming story about your boss at his retirement, but maybe not if it's a drunken roast. The tone needs to match the speech itself and the occasion.  Who is the audience for the speech? What are their expectations of the speech and the speaker? How would you describe the tone of the speech? Did it match the content? How? If not, how might the tone be improved? How well will the tone match the audience for the speech?
Summary:
Evaluate the content of the speech. Evaluate the organization of the speech. Evaluate the style of the speech. Evaluate the tone of the speech.