Parallelogram Verification: Quadrilateral ABCD with Sides 15, 12, 7, and 8

Question

Look at the quadrilateral ABCD.

AB = 15

CD = 12

BD = 7

AC = 8

Is this quadrilateral a parallelogram?

Video Solution

Solution Steps

00:13 Our question is: Is the quadrilateral a parallelogram?

00:18 A parallelogram has two pairs of equal opposite sides.

00:22 Let's check the sides of our quadrilateral now.

00:26 Oh! The opposite sides aren't equal, so it's not a parallelogram.

00:30 And that's how we solve this problem!

Step-by-Step Solution

To determine whether the quadrilateral ABCD is a parallelogram, we must establish whether both pairs of opposite sides are equal. In a parallelogram, this criterion is met: the opposite sides are congruent.

First, we compare the lengths of the opposite sides:

Length $AB = 15$ and length $CD = 12$ . These two sides are not equal.
Length $AC = 8$ and length $BD = 7$ . These two sides are also not equal.

Since neither pair of opposite sides is equal, quadrilateral ABCD does not satisfy the conditions for being a parallelogram.

Therefore, the solution to the problem is that quadrilateral ABCD is not a parallelogram.

$\boxed{\text{No}}$

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