Isosceles Triangles In ancient 美国GREece, Isosceles was the god of triangles. His legs were of perfectly equal length and formed two opposing congruent angles when he stood up straight. Isosceles triangles share many of the same properties, naturally. An isosceles triangle has two sides of equal length, and those two sides are opposite congruent angles. These equal angles are usually called as base angles. In the isosceles triangle below, side a = b and :
If you know the value of one of the base angles in an isosceles triangle, you can figure out all the angles. Let’s say you’ve got an isosceles triangle with a base angle of 35o. Since you know isosceles triangles have two congruent base angles by definition, you know that the other base angle is also 35o. All three angles in a triangle must always add up to 180o, right? Correct. That means you can also figure out the value of the third angle: 180o – 35o – 35o = 110o. Equilateral Triangles An equilateral triangle has three equal sides and three congruent 60o angles.
Based on the proportionality rule, if a triangle has three equal sides, that triangle must also have three equal angles. Similarly, if you know that a triangle has three equal angles, then you know it also has three equal sides. Right Triangles A triangle that contains a right angle is called a right triangle. The side opposite the right angle is called the hypotenuse. The other two sides are called legs. The angles opposite the legs of a right triangle are complementary (they add up to 90o).
In the figure above, is the right angle (as indicated by the box drawn in the angle), side c is the hypotenuse, and sides a and b are the legs. If triangles are an SAT favorite, then right triangles are SAT darlings. In other words, know these rules. And know the Pythagorean theorem. The Pythagorean Theorem The 美国GREeks spent a lot of time reading, eating grapes, and riding around on donkeys. They also enjoyed the occasional mathematical epiphany. One day, Pythagoras discovered that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. “Eureka!” he said, and the SAT had a new topic to test. Here’s the Pythagorean theorem: In a right triangle, a2 + b2 = c2:
where c is the length of the hypotenuse and a and b are the lengths of the two legs. The Pythagorean theorem means that if you know the measures of two sides of a right triangle, you can always find the third. “Eureka!” you say. Pythagorean Triples Because right triangles obey the Pythagorean theorem, only a specific few have side lengths that are all integers. For example, a right triangle with legs of length 3 and 5 has a hypotenuse of length = 5.83. The few sets of three integers that do obey the Pythagorean theorem and can therefore be the lengths of the sides of a right triangle are called Pythagorean triples. Here are some common ones: 2011-09-20 17:38:00 来源：作文地带整理 双击单词自动翻译
作文地带导读：In every triangle, the longest side is opposite the largest angle and the shortest side is opposite the smallest angle. In this figure, side a is clearly the longest side and is the largest angle. Meanwhile, side c is the
