Shikhakaushal

Introduction to Algebra Algebra is great fun - you get to solve puzzles! A Puzzle What is the missing number?   − 2 = 4 OK, the answer is 6, right? Because  6 − 2 = 4 . Easy stuff. Well, in Algebra we don't use blank boxes, we use a  letter  (usually an x or y, but any letter is fine). So we write: x − 2 = 4 It is really that simple. The letter (in this case an x) just means "we don't know this yet", and is often called the  unknown  or the  variable . And when we solve it we write: x = 6 Why Use a Letter?   Because: it is easier to write "x" than drawing empty boxes (and easier to say "x" than "the empty box"). if there are several empty boxes (several "unknowns") we can use a different letter for each one. So  x  is simply better than having an empty box. We aren't trying to make words with it! And it doesn't have to be  x , it could be  y  or  w  ... or any letter or symbol

Interior Angles of Polygons An Interior Angle is an angle inside a shape Another example: Triangles The Interior Angles of a Triangle add up to 180° Let's try a triangle: 90° + 60° + 30° = 180° It works for this triangle Now tilt a line by 10°: 80° + 70° + 30° = 180° It still works! One angle went  up  by 10°, and the other went  down  by 10° Quadrilaterals (Squares, etc) (A Quadrilateral has 4 straight sides) Let's try a square: 90° + 90° + 90° + 90° = 360° A Square adds up to 360° Now tilt a line by 10°: 80° + 100° + 90° + 90° = 360° It still adds up to 360° The Interior Angles of a Quadrilateral add up to 360° Because there are 2 triangles in a square ... The interior angles in a triangle add up to  180°  ... ... and for the square they add up to  360°  ... ... because the square can be made from two triangles! Pentagon A pentagon has 5 sides, and can be made from  three triangles , so you know what ... ...