Why do we need undefined terms

What is a point in math? A point in geometry is a location. It has no size i. A point is shown by a dot. A line is defined as a line of points that extends infinitely in two directions. It has one dimension, length. What makes a point undefined? In Geometry, we have several undefined terms: point, line and plane. From these three undefined terms, all other terms in Geometry can be defined.

In Geometry, we define a point as a location and no size. And the third undefined term is the line. So let's go back and define these as much as we can. What is perpendicular line?

In elementary geometry, the property of being perpendicular perpendicularity is the relationship between two lines which meet at a right angle 90 degrees. A line is said to be perpendicular to another line if the two lines intersect at a right angle. Why is a plane undefined? When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection.

Point of intersection means the point at which two lines intersect. Given figure illustrate the point of intersection of two lines. We can find the point of intersection of three or more lines also. For two lines to intersect, each of the three components of the two position vectors at the point of intersection must be equal.

Therefore we can set up 3 simultaneous equations, one for each component. What are skew lines? Skew lines are two or more lines that do not intersect, are not parallel, and are not coplanar.

Remember that parallel lines and intersecting lines lie on the same plane. This makes skew lines unique — you can only find skew lines in figures with three or more dimensions.

If the solution is not in the unit square, the segments do not intersect. If you are talking about ordinary lines and ordinary geometry, then parallel lines do not meet. Calculus relies heavily on these two skills. This won't be easy. Before we go too deep into the actual Geometry, we need to introduce some terms that we'll use in order to help solve problems and prove scenarios.

Think of these terms as the building blocks of Geometry. Without these, we're stuck. An undefined term is a term that can't be defined so easily. There really isn't a definition to define such terms. Consider the word "the. We can describe these terms, but we can't provide an actual definition.

There are terms in Geometry that can't be defined so easily. We'll go over those later. A defined term is, simply put, a term that has some sort of definition. Unlike "the" and "am", we can put a definition to the word "she. Simple, right? In Geometry, we can use undefined terms to define a term. I like to call these statements the "well, duh" statements.

These statements are "facts" that are accepted without proof. We can't approach proving these statements using conventional means. These statements are so basic that we can't use true technical jargon to explain them. However, if we use a little bit of critical thinking, we can use undefined and defined terms to help support a postulate. Now the third undefined term is a line. And a line is set of points or, the word that you might learn later is locus, extending in either direction infinitely.

So a line is going to be all the points, and we can actually select two of them to name it. So we can call this Line AB. Now when you're labeling a line, it's key to include at least two points. Or if you have some sort of smaller letter over here, we can call this Line L.

But notice how I'm writing the arrows above my letters; I have arrows on either side. And these arrows tell you, the geometry student, that it extends infinitely in this direction. Now this arrow here extends infinitely in that direction. You can have points be collinear, that is, they share the same line. So here we could have, C, D, and E are all collinear. And if you look at Point F here, I drew this in to draw a contrast.