If ABCD is a parallelogram, what can we say about the diagonals BD and AC?

A. They bisect each other.
B. They are congruent.
C. They are congruent to sides AD and BC.
D. They are congruent to sides AB and DC.

Question

25-11-2024
Mathematics

High School

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If ABCD is a parallelogram, what can we say about the diagonals BD and AC?

A. They bisect each other.
B. They are congruent.
C. They are congruent to sides AD and BC.
D. They are congruent to sides AB and DC.

Answer :

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poonamyadav poonamyadav · Answer 1 · 2023-12-24T13:52:48-05:00

Final answer:

In a parallelogram, the diagonals bisect each other but are not necessarily congruent. Also, they are not congruent to the sides of the parallelogram.

Explanation:

In a parallelogram ABCD, the properties of the diagonals AC and BD are quite fascinating. For starters, they bisect each other. This means that if diagonals AC and BD intersect at point E, then AE = EC and BE = ED. Diagrammatically, it forms four triangles AEB, BEC, CED, and DEA that have equal areas. However, these diagonals are not necessarily congruent in a general parallelogram. They will be congruent only if the parallelogram is a rectangle.

Furthermore, these diagonals are not congruent to the sides of the parallelogram. The rule that attests to this statement is, the diagonal of a parallelogram separates it into two congruent triangles. Therefore, triangles such as ∆AEB and ∆CED are equivalent, but AE or EB (portions of the diagonal) does not parallel or equate to any side of the parallelogram ABCD.

Learn more about Parallelogram Diagonals here:

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If ABCD is a parallelogram, what can we say about the diagonals BD and AC?A. They bisect each other.B. They are congruent.C. They are congruent to sides AD and BC.D. They are congruent to sides AB and DC.

Answer :

Final answer:

Explanation:

Learn more about Parallelogram Diagonals here:

Other Questions

If ABCD is a parallelogram, what can we say about the diagonals BD and AC?

A. They bisect each other.
B. They are congruent.
C. They are congruent to sides AD and BC.
D. They are congruent to sides AB and DC.