Properties of parallelograms often show up in geometric proofs and problems. Parallelogram properties apply to rectangles, rhombi and squares. In a parallelogram, opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary and diagonals bisect each other. Other important polygon properties to know are trapezoid properties, and kite properties.
Properties of quadrilaterals show up all over geometry, in proofs, in true and false questions, in multiple choice and fill in the blank. So it is really good to know the properties of various quadrilaterals.
Parallelograms have properties that apply to rectangles, rhombi and squares. So whatever we decide that parallelograms have as properties is going to apply to those three parallelograms as well.
First key thing is opposite sides are congruent. Well, if I look at opposite sides, I'm going to mark those two sides as being congruent to each other. But how do we know this is a parallelogram? Definition of a parallelogram is that we have two pairs of parallel sides. So notice in a parallelogram that all four sides don't need to be congruent. If they were, that would be a rhombus.
The second key thing is that the opposite angles are congruent. So if I look at this angle right here, it's opposite. Basically, if I drew a diagonal, where would that angle be? So opposite angles are congruent. I will mark these two angles as being congruent to each other but not congruent to the other consecutive angles.
The next thing is consecutive angles are supplementary. If I call this angle X and this will be angle Y. So this will be X and this will be Y. No matter how I looked at these consecutive angles, X plus Y, they are going to equal 180 degrees. Why is that? If I have two parallel lines, this side of here can be thought of as a transversal, we have same side interior angles which are always supplementary. Same can be said for these two parallel lines where we have a transversal. So no matter how I look at this, I'm going to have same side interior angles.
And the last key thing is that the diagonals will bisect each other. So I'm going to draw that in in a different color marker. So if I drew in a diagonal right here and if I drew in another diagonal, there is only two diagonals in a parallelogram, notice these are not going to be congruent to each other. But what will happen is that this point right here will bisect that diagonal into two congruent pieces and this point will bisect the other diagonal. So I will use -- one, two, three -- four markings to show that this is bisected.
So you are going to apply this knowledge in proofs, in problems and in true and false and fill in the blank questions.