What is the name for a parallelogram in which two adjacent sides are equal in length?
Let’s see if we can sketch something that fits this description. A parallelogram has two sets of parallel sides. Here’s one set of parallel lines. And here’s a second set of parallel lines. We also know that two adjacent sides are equal in length. Adjacent sides share a vertex. They share a point.
If two adjacent sides are equal in length, let’s say they both measure five centimetres, in order for these two pink lines to be parallel, they must be the same distance from each other at every point. They are five centimetres apart at the bottom. And that means they must be five centimetres apart at the top. Because we know that the two yellow lines are parallel, then this pink line must also measure five centimetres.
From the information we’re given, we can say that we have a parallelogram with four equal side lengths. And that is the definition of a rhombus. A parallelogram with four equal side lengths is a rhombus.