Quadrilateral Analysis: Testing Parallelogram Properties with Sides 10, 8 and Diagonals 2, 4

Question

Below is the quadrilateral ABCD.

AB = 10 and CD = 8.

BD = 2 and AC = 4.

Is the quadrilateral a parallelogram?

Video Solution

Solution Steps

00:00 Is the quadrilateral a parallelogram?

00:03 A parallelogram is a quadrilateral with 2 pairs of equal opposite sides

00:07 Let's check the sides of our quadrilateral, according to the given data

00:11 Opposite sides are not equal, therefore it's not a parallelogram

00:16 And this is the solution to the question

Step-by-Step Solution

To determine if quadrilateral $ABCD$ is a parallelogram, we apply the condition that a parallelogram has both pairs of opposite sides congruent.

We are given:

Side $AB = 10$ .
Side $CD = 8$ .

To be a parallelogram, not only should $AB = CD$ , but $AD$ should be equal to $BC$ . However, the provided lengths don't satisfy this condition.

No further information is presented about the length equality of sides $AD$ and $BC$ , nor do provided diagonals imply certain conditions towards opposite sides equality.

Since $AB \neq CD$ , we immediately conclude the quadrilateral fails to meet the requirement of having both pairs of opposite sides equal as needed for it to be a parallelogram.

Therefore, the quadrilateral $ABCD$ is not a parallelogram.

Conclusion: No

Answer

Related Subjects

Identifying a Parallelogram

Question Types

Identifying a Parallelogram: Using the theorem: If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is considered a parallelogram