Identifying a Parallelogram

Do you want to know how to identify a parallelogram from miles away?
After this article, you will be sure to immediately know when it refers to a parallelogram and when to another square..
In order to make it easier for you to identify a parallelogram, we will divide the five identification sentences into 3 key expressions:

• Sides of the square
• Diagonals of the square
• Angles of the square

Wonderful.
Let's start with the first expression:

1) In a square where each pair of opposite sides are parallel to each other, the square is a parallelogram.

Parallelogram

We ask ourselves, are each pair of opposite sides also parallel in the square we have in front of us?
If the answer is affirmative, we can determine that it is a parallelogram.

2) In a square where each pair of opposite sides are equal to each other, the square is a parallelogram.

We ask ourselves, are each pair of opposite sides equal in the square we have in front of us?
If the answer is yes, we can determine that it is a parallelogram. Pair of opposite sides.
Note that these are theorems that describe a condition that exists in $2$ pairs of opposite sides.
That is, if we have data on $2$ pairs of opposite sides, both equal or parallel - we can determine that it is a parallelogram.

If we have data on only one pair of opposite sides in a square, we can use the third theorem of this key expression:

3) If a square has a pair of opposite sides that are equal and parallel, the square is a parallelogram.

In this theorem, the pair of opposite sides must be parallel and equal, but only one of those pairs is sufficient.

We ask ourselves, is there a pair of opposite sides that are both equal and parallel in the square we have in front of us?
If the answer is affirmative, we can determine that it refers to a parallelogram.

Now, let's move on to the second key expression:

In this expression, there is only one theorem that talks about the diagonals of the square:
4) If in a square, the diagonals that intersect the square are parallel.
Remember: intersecting diagonals are diagonals that intersect each other. Exactly in the middle!

We wonder, do the diagonals intersect (exactly in the middle) in the square we have in front of us?
If the answer is yes, we can determine that it refers to a parallelogram.
Now, let's move on to the third key expression:

If in a square there are two pairs of equal opposite angles, the square is a parallelogram.

We ask ourselves, are there two pairs of equal opposite angles in the square we have in front of us?
If the answer is affirmative, it is determined to be a parallelogram.

Tip:
To remember all the theorems, try to remember the key expression and remember that there are a total of $5$ sentences that will help us identify that it is a parallelogram.

If you are interested in this article, you might also be interested in the following articles:

Parallelogram - Checking the parallelogram

The area of the parallelogram: What is it and how is it calculated?

Rotational symmetry in parallelograms

In the blog of Tutorela you will find a variety of articles about mathematics.