Proving Congruency: The Four Sides of a Parallelogram are Equal in Length

A parallelogram has four congruent sides

To prove that a parallelogram has four congruent sides, we can use the properties of a parallelogram

To prove that a parallelogram has four congruent sides, we can use the properties of a parallelogram.

A parallelogram is a quadrilateral with opposite sides that are parallel and congruent. This means that both pairs of opposite sides are equal in length.

Let’s denote the sides of the parallelogram as AB, BC, CD, and DA.

Since AB and CD are opposite sides of the parallelogram and parallel, they are congruent. Similarly, BC and DA are also opposite and parallel, making them congruent as well.

So, we have AB ≅ CD and BC ≅ DA.

Now, we need to prove that all four sides are congruent.

To do that, we can use the property that opposite sides of a parallelogram are equal in length.

Since AB and CD are equal, and BC and DA are equal, by transitive property, we can conclude that AB ≅ BC ≅ CD ≅ DA.

Therefore, all four sides of the parallelogram are congruent.

More Answers: