A parallelogram is just one type of polygon. It is a quadrilateral that has opposite sides that are parallel to one another. To determine if the quadrilateral you’re working with is a parallelogram, you need to know the following 6 properties of parallelograms.
Opposite Sides Are Parallel
Parallel lines are lines that are always the same distance apart and never touch. If the sides of a parallelogram were lines that continued on, the ones opposite of each other would never touch. These lines would remain the same distance away from each other no matter how far they extended. If your quadrilateral has opposite sides that are parallel, then you may have a parallelogram.
Opposite Sides Are Congruent
In geometry, congruent means that two things are identical. If you were to superimpose the shapes on top of each other they would match up exactly. This is true for a parallelogram’s sides. Each of the opposite sides are the same in length. If you were to break the shape apart and place the opposite sides on top of each other, you would find that they line up perfectly.
Opposite Angles Are Congruent
The angles that are opposite of each other are also congruent. To find out if your quadrilateral is a parallelogram, you could get out your protractor and measure each angle. The angles opposite of each other will have the same measurement. It’s common for a parallelogram to have two acute angles and two obtuse angles. Therefore, the acute angles should have the same measurement, and the obtuse angles should also have the same measurement.
Consecutive Angles Are Supplementary
To find another one of the properties of parallelograms, draw an imaginary line through the shape to cut it in half. Then, look at the consecutive angles (or the ones that are next to each other). If the shapes are supplementary, then the shape might be a parallelogram.
Supplementary angles are two angles that add up to 180-degrees. Let’s say that two of the consecutive angles have measurements of 35-degrees and 145-degrees. If we add these together (35 + 145), the sum is 180-degrees. Therefore, we have supplementary angles.
Diagonals Bisect Each Other
Now pretend to draw an imaginary line from one angle to its opposite, congruent angle. This line should create two congruent triangles within the shape.
From there, proceed to draw another imaginary line from the supplementary angle to its opposite, congruent angle. These two imaginary lines should bisect one another. (To bisect is to cut something into two equal parts.) If this is the case with the diagonal lines, then (along with the previous five properties) you have a parallelogram.
If One Angle Is a Right Angle…
The last property only matters if there is a right angle in your quadrilateral. If you have one angle that is a right angle, then all the rest of the angles should be right angles, too. Why? Because we know that the opposite angles are congruent. We also know that consecutive angles are supplementary, and 90 + 90 = 180. Therefore, all four angles would have a measurement of 90-degrees.
Let’s recap. You’ll know that your quadrilateral is a parallelogram if it has these properties of parallelograms:
1. The opposite sides are parallel.
2. The opposite sides are congruent.
3. The opposite angles are congruent.
4. Consecutive angles are supplementary (add up to 180-degrees).
5. The diagonals bisect each other.
6. And all four angles measure 90-degrees IF one angle measures 90-degrees.
Look for these 6 properties of parallelograms as you identify which type of polygon you have.