Parallelograms

Mentor: Does anyone recall or know what we call it when 2 lines run side-by-side and never cross?

Student: Yes. Lines like that are called parallel lines.

Mentor: Great! We've already learned that quadrilaterals have how many sides?

Student: Four.

Mentor: That's right and we call quadrilaterals with parallel sides parallelograms.

Student: But, how can all the sides be parallel if a quadrilateral is a polygon and is all closed off?

Mentor: Great thinking! I guess what I should have said is that a parallelogram has two pairs of opposite sides that are parallel, like this:

Student: Oh, so the top is parallel to the bottom and the sides are parallel to each other. I understand now!

Mentor: Good. Now I want to tell you about a special kind of parallelogram. It's called a rhombus. A rhombus is a parallelogram, but all four sides have the same length.

Student: So a rhombus is a type of parallelogram just like a banana is a type of fruit.

Mentor: Right, we should not say that all parallelograms are rhombii, just like we don't say that all fruits are bananas.

Student: I think I understand what parallelograms and rhombii are.

Mentor: Wonderful! Now we can talk about rectangles!