Parallelism

First we are going to talk about parallelism. Parallelism is the relationship between two geometric figures in which they never intersect. Parallelism is used mostly on lines. It is also used on other geometric figures as well. In here, we are going to talk about parallelism mainly regarding lines. In space there exist three possible relationships between two lines: intersecting lines, parallel lines, and skew lines.

If two lines are parallel, they are never intersecting; if two lines are intersecting, they are never parallel; if two lines are skew, they are not in one plane or coplanar. There are quite a few theorems used to prove that two lines are parallel. Please click here to see these theorems. I have also provided a sample proof below to prove that two lines are parallel.

Conditional Statements

Now we are going to talk about conditional statements. Conditional statements have nothing directly to do with geometry. But they are used everywhere in people's lives. Then what exactly are conditional statements? Remember that you might have been always saying that if you weren't doing one thing then you were going to do another thing? This is a conditional statement. Conditional statements are used to determine whether an expressed idea is true or false. Read the following conditional statement:

"If I am going to study for the test, then I am going to do well on it."

In this statement, the first part of the sentence is called a statement or p; the second part of the sentence is called the negation of p or ~p. This statement is a conditional statement, and we write it as p®q. A conditional statement is always true. The converse of a conditional statement is written as q®p, and it may not always be true. The relations between p and q are listed below:

P	Q	P ® Q
T	T	T
T	F	F
F	T	T
F	F	T

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