Basic Geometrical Concepts for Students

Video Transcript

"Hi, in this clip I would like to show you some basic geometrical concepts and formulas that will be of use to you when you're working on those pesky word problems. So we'll start out with triangles. In this triangle, we have the base being B, the height being H, and the other two sides being A and C. The area of any triangle with a Height H and Base B is given by one half the base times the height. Another formula that may come in handy when referring to triangles is the perimeter of a triangle, and in the perimeter, you just add up the three sides of the triangle, so the perimeter is A plus B plus C. A special type of triangle that you may run into often is the right triangle. This is a triangle which has a right angle as one of its angles; oftentimes, denoted by the little box in the angle. Now for right triangles, not only do we have the previous formulas of the area is one half the base times the height, and the perimeter is the sum of the sides of the triangle, but we also have the celebrated Pythagorean Theorem. Okay, so the Pythagorean Theorem tells you exactly when the sides of the right, of a triangle give you a right triangle, and that is when A squared plus B squared equals C squared. Another situation which may come into play is when you have a couple of triangles that are what Mathematicians call similar triangles. Similar triangles have angles that are equal. In this picture, we have two triangles where the angles match. Whenever you have similar triangles, geometry tells you that the ratio of the sides have to be equal. So for instance, the ratio of R to S must equal the ratio of L to M, and we can write that this way. Given this ratio; this equality of ratios, one could solve for any of those variables needed in a particular word problem that you're working. These are some basic geometrical formulas that'll come in handy any time that you're working some word problems, or working out in the real world at where you have any kind of geometrical figures."