Question Video: Determining Which of a Set of Given Letters Has Parallel Lines | Nagwa Question Video: Determining Which of a Set of Given Letters Has Parallel Lines | Nagwa

Question Video: Determining Which of a Set of Given Letters Has Parallel Lines Mathematics

>Which of the following letters has parallel lines: Y, F, A, L?

03:01

Video Transcript

Which of the following letters has parallel lines: Y, F, A, or L?

Now, we know when two lines are parallel, they’re always the same distance apart. So when we look at them, they look like they’re going in exactly the same direction. These two lines are parallel, so are these. But we couldn’t say that these two lines are parallel because these aren’t always the same distance apart. Now, in our question, we’re given some capital letters to look at. And we’re asked which one of them has parallel lines. Now, to help us answer the question, let’s write these capital letters really big. And we’re going to use a different color for each line that makes up the letter.

To begin with, we’ve got the letter Y. Now, we can write the letter Y by drawing a straight line up like this and two lines at the top that make a sort of V shape. Now can you see any pairs of lines in this letter that are always the same distance apart, they never touch, and they’re going in the same direction? We can’t, can we? If we look at the pink line and the orange line, well, they’re touching, and they’re not the same distance apart. And the same is true of the green line and the orange line. And even if we look at the pair of lines that make the V shape, that’s the pink line and the green line, we can see that the distance between them isn’t always the same at all. The letter Y doesn’t have any parallel lines.

What about the letter F? We can write a capital F by drawing a straight line upwards and then two shorter horizontal lines. Can you see any parallel lines in this letter? If we look at the orange line and the pink line to begin with, we can see that they meet at a right angle. They’re not parallel, but we could describe them as being perpendicular. Unfortunately, though, we’re not looking for perpendicular lines, which is a shame because the orange line and the green line are perpendicular too.

Now, what if we compare the green line and the pink line? We can see that they are always the same distance apart, and they do go in the same direction. These two lines are parallel. And we can show that they’re parallel by drawing little arrow heads, one on each line. Wherever we see lines labeled like this, we know they’re parallel. Looks like we found our answer, doesn’t it? Let’s just check the other letters.

We can see that in the letter A, none of the lines are parallel. And the two lines that make up the letter L aren’t parallel either. We could say they’re perpendicular, though. They meet at a right angle, don’t they? Out of the four letters that we’re given, the one that has parallel lines is the letter F. And if you get a spare moment, why not see if there are any other letters of the alphabet that have parallel lines, too?

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