Question

The diagonals of quadrilateral ABCD intersect at point K. Is each statement needed to prove that ABCD is a parallelogram?
BK = AK
BK = DK
CK = AK
CK = DK

Answer 1

Answer:

Therefore to prove that ABCD is a parallelogram we need,

BK = DK

CK = AK

Step-by-step explanation:

Given:

The diagonals of quadrilateral ABCD , intersect at point K.

To Find:

Which statement needed to prove that ABCD is a parallelogram?

Solution:

For a Quadrilateral to be a Parallelogram,

• Diagonals Bisect each other.
• Opposite Sides are Parallel and Equal.
• Opposite angles are equal.

Here Diagonals intersect at K

∴ BK = DK            ......K bisect Diagonal BD

∴ CK = AK            ......K bisect Diagonal AC

Therefore to prove that ABCD is a parallelogram we need,

BK = DK

CK = AK

Answer 2

In this exercise we have to use the knowledge of quadrilaterals to prove that the diagonals form a parallelogram, so we can say that:

$BK = DK CK = AK$

Given the following information we have that for a quadrilateral to be a parallelogram, will have:

• Diagonals Bisect each other.

• Opposite Sides are Parallel and Equal.

• Opposite angles are equal.

• Here Diagonals intersect at K

So, with this information we have:

$BK = DK \rightarrow K bisect Diagonal BD CK = AK \rightarrow K bisect Diagonal AC$

See more about parallelogram at brainly.com/question/1563728