SAT数学知识讲解：三角形一.doc

SAT数学知识讲解：三角形一 小马过河为大家准备了“SAT数学知识讲解：三角形一”，供各位备考SAT的考生们参考使用，来提高自己的托福成绩！免费咨询电话：400-0123-267 　　Triangles pop up all over the Math section. There are questions specifically about triangles, questions that ask about triangles inscribed in polygons and circles, and questions about triangles in coordinate geometry. 　　Three Sides, Four Fundamental Properties 　　Every triangle, no matter how special, follows four main rules. 　　1. Sum of the Interior Angles 　　If you were trapped on a deserted island with tons of SAT questions about triangles, this is the one rule you’d need to know: 　　The sum of the interior angles of a triangle is 180°. 　　 　　If you know the measures of two of a triangle’s angles, you’ll always be able to find the third by subtracting the sum of the first two from 180. 　　2. Measure of an Exterior Angle 　　The exterior angle of a triangle is always supplementary to the interior angle with which it shares a vertex and equal to the sum of the measures of the remote interior angles. An exterior angle of a triangle is the angle formed by extending one of the sides of the triangle past a vertex. In the image below, d is the exterior angle. 　　 　　Since d and c together form a straight angle, they are supplementary: 　　 　　. According to the first rule of triangles, the three angles of a triangle always add up to 　　 　　, so 　　 　　. Since 　　 　　and 　　 　　, d must equal a + b. 　　3. Triangle Inequality Rule 　　If triangles got together to write a declaration of independence, they’d have a tough time, since one of their defining rules would be this: 　　The length of any side of a triangle will always be less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides. 　　There you have it: Triangles are unequal by definition. 　　Take a look at the figure below: 　　 　　The triangle inequality rule says that c – b a c + b. The exact length of side a depends on the measure of the angle created by sides b and c. Witnes