Which of the following shapes has only three sets of parallel lines?
We know that parallel lines are lines that never intersect. We often mark parallel lines with these type of arrows. When you see two arrows, it’s parallel to the other line that has two arrows. Let’s consider the five shapes we were given.
Shapes b and c have no markings. This is because b and c have zero sets of parallel lines. They don’t have parallel lines because they have an odd number of sides. A triangle has three sides and can’t have any parallel lines. A pentagon has five sides and also has no sets of parallel lines. So we will cross out these two options.
Remember how I said that the number of arrows mattered. These two sides have one arrow each. And it tells us that these two sides are parallel with each other. That’s one set of parallel lines. And then, we look at the place that has two arrows. These two sides are parallel with each other.
Next, we find the two sides that have three arrows each. We can also tell that they are directly across from each other. Here’s our third set of parallel lines for shape a. Shape a has a fourth set of parallel lines that has four arrows each. These two green lines make up the fourth set of parallel lines. This octagon is made up of four sets of parallel lines. And we’re looking for the shape that has three sets. The octagon is not that shape. Looking at the square, we find that the square has two sets of parallel lines.
And finally, we come to the hexagon. The sides with one arrow are parallel to each other. The sides with two arrows are parallel to each other. And the sides with three arrows are parallel with each other. The hexagon has three sets of parallel lines. This is the shape we were looking for.