Geometry is one of the most fascinating and widely used branch of mathematics. It is quite understandable since everything you have to know can be seen from sketches or constructions. The word “geometry” derived from the Greek word for “earth measure” which means that geometry is a science that can be derived from observing things around us. By learning geometry you will learn how to observe things and conclude things you want to know using one or more important statements. Theorems, lemmas and statements in this field come very natural to us, so they are not that hard to remember.
Isometry is a transformation (the same as function) which preserves measurements, more specifically
Ellipse is the set that contains all points of the plain for which the sum of the distances...
For an ellipse construction, focal points must be given...
Every ellipse is uniquely defined by its axes and the coordinates of its focuses.
Line and ellipse can be found in three different relation: two points, one point, no points.
Hyperbola is not a closed curve, but its parts are in a way bounded by two lines – asymptotes.
The definition and basics of a circle Let $S$ be a fixed point in the plane and $r>0$. A circle
Solid figures are three dimensional figures. The most common solids are prism, cylinders, pyramids
Triangles, Quadrilaterals, Pentagons, Hexagons, Heptagons, Octagons, Nonagons etc. are known as polygons.
Quadrilaterals are part of a plane enclosed by four side (quad means four and lateral means side).
Similarity assume that angles of two triangles must be equal and lenghts of sides proportional.
The triangle inequality says that one side in a triangle must be lesser than the sum of other two.
How to construct angle bisector? What is median and centroid? How to use Triangle Inequality Theorem?
The right triangle is a triangle that has right angle. There are important theorems like Pythagorean
Two or more triangles are congruent if they have 3 sets of congruent sides and 3 sets of congruent angles.
What type of triangles are there? How to construct triangle? What The Exterior Angle Theorem represents?
Basics about line segment, measure an acute, obtuse, right, straight, reflex angles in cm, mm or radians.
Is there an easier way to start?
If you are new to geometry, it is a good thing to start from the very basics. Start by drawing a line and studying it. This may seem like a trivial thing to do but you’ll come to a realization that it actually isn’t. You may start to realize that that line actually has many properties. Now draw another line. Look at their relation. Do they intersect? Are they parallel? Now you have an object more, and more relations to look at. If they intersect they are enclosing four angles. What do those angles have in common and what not? If you continue like this you will start noticing that there is much more to it than simple lines. Now get some piece of paper and scissors. Cut out many different triangles and study their relation. What is different about them and what is the same? Remember, geometry isn’t something you can learn simply by remembering some rules and trying everything out, it should be tested and drawn and imagined.
Learning about different shapes
Many people have the tendencies that when somebody speaks about geometry a big triangle pops into their minds. That is not without a reason. There are many properties of triangles we know of, starting from their surface, their angles, construction, congruency and many more. We study them the most because every other shape can be divided into triangles, and since we know their properties it is no problem to calculate properties of any other shape. Of course, sometimes it is easier to memorize some properties of different shapes than to calculate over triangles. This will be true for right polygons. Another important figure in plane geometry is a circle. You may think that circle is quite simple and there isn’t really much to know about it but that isn’t true at all. In these lessons you won’t be learning only the basics of circles, but some advanced things also.
Moving onto the next dimension
Every plane figure has its 3D generalization. For example, try to cut out many identical squares and stack them one on another. Then do the same with triangles. You will start seeing real 3D objects. You will see that any object you learned until now can be stacked like this and you will create a 3D object. These objects you created all have different but similar properties. You will learn a bit easier way to visualise them using their grids.
Now try something different: cut out a circle and hang it on a thread. Lightly blow on one side and look at it. You will be seeing a sphere. Everywhere you look around you will be seeing some solid figure. Here you can learn to calculate everything you ever wanted to know about it.