In the parallelogram KLMN, the diagonal KM is 7 inches long. How long would LN have to be to ensure that KLMN is a rectangle?
aren't the diagonals in a rectangle equal?
recall that the diagonals of a rectangle are equal.
To determine the length of LN that would ensure KLMN is a rectangle, we first need to understand some properties of a parallelogram and a rectangle.
In a parallelogram, opposite sides are parallel and congruent, while opposite angles are also congruent. In a rectangle, all angles are right angles (90 degrees).
To convert a parallelogram into a rectangle, we need to make sure that the diagonals are congruent and intersect at right angles.
In this case, we are given the length of diagonal KM as 7 inches. To find the length of LN, we need to determine if KM and LN are congruent diagonals.
To do this, we can use the properties of parallelograms. Since KLMN is a parallelogram, we know that opposite sides are parallel and congruent. This means that KN is congruent to LM and KL is congruent to MN.
Since KM is a diagonal, it intersects both KN and LM. Therefore, we can conclude that KM is congruent to KN and LM. So, KM is also congruent to LN, as LN is parallel to KL.
Now that we know KM is congruent to LN, we can use the given length of KM (7 inches) to find the length of LN. Since KM and LN are congruent, LN must also be 7 inches long.
So, to ensure that KLMN is a rectangle, LN would have to be 7 inches long.