The great advantage of listing properties is that we can see the relationships among them immediately. A trapezium is a quadrilateral in which one pair of opposite sides are parallel.ĭraw a few parallellograms, a few rhombuses (correctly called rhombii, like cactus and cactii) and a few trapeziums (correctly written trapezia).
A rhombus is a quadrilateral in which opposite sides are parallel and all sides are equal.ģ. A parallelogram is a quadrilateral in which opposite sides are parallel and equal.Ģ. This suggests a way of classifying quadrilaterals, of grouping them according to whether some sides are equal or not, some angles are equal or not. Thus we see that every square is a rectangle but a rectangle need not be a square. (4) Now we can combine (1) and (4) and say that in a square, all sides are equal. A square has all these properties but the third is replaced by Adjacent sides are equal. (3)Īmong these, the last statement really says nothing! (Mathematicians call such statements trivial, and they prefer not to write them down.) Note that adjacent sides have a vertex in common, and opposite sides have no vertex in common. O Adjacent sides may or may not be equal. O All angles are equal, each is 90 degrees. We know rectangles, so we can ask what properties rectangles have. The best way to answer this is to go back to what we already know and look at it from this viewpoint. We call them quadrilaterals.ĭo you see some patterns in all the data you have recorded? We see many interesting properties, but how do we know whether these are true in general, or happen to hold only for these figures? It is not even clear what properties we should look for. Here are some examples of 4-sided polygons. Squares and rectangles are examples of polygons with 4 sides but they are not the only ones. Two ? But how can you get a closed shape with two sides? Three? Yes, and this is what we know as a triangle. How many sides can a polygon have? One? But that is just a line segment. The word poly stands for many, and a polygon is a many-sided figure. The sides are line segments joining the vertices. We call these points vertices of the polygon. How do polygons look? They have sides, with points at either end. We need names to call such closed shapes, we will call them polygons from now on. The other three are closed shapes made of straight lines, of the kind we have seen before. We observe that the first is a single line, the four points are collinear.
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