In triangles, we talked of equilateral triangles as those with all sides equal. When all angles of a quadrilateral are equal, we call it equiangular . When all sides of a quadrilateral are equal, we call it equilateral. For instance, we see that a rhombus is a parallelogram in which all sides are also equal. (Do you see why?) Now we can observe many more interesting properties. A smart question then is: just when is the other way also true? For instance, when is a parallelogram also a rectangle? Any parallelogram in which all angles are also equal is a rectangle. O Every square is a rhombus and hence every square is a parallelogram as well.įor “not necessarily the other way” mathematicians usually say “the converse is not true”. O Every rectangle is a parallelogram, but not necessarily the other way. O Every rhombus is a parallelogram, but not necessarily the other way. O Every parallelogram is a trapezium, but not necessarily the other way. 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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