Question

1. in parallelogram abcd, the diagonals intersect at point e. which equation correctly represents the relationship between ed and bd?

options:
ed + bd = 180
\frac{1}{2}(ed) = bd
2(ed) = bd
ed = bd

Explanation:

Step1: Recall parallelogram diagonal property

Diagonals of a parallelogram bisect each other. So, point E divides BD into two equal parts: ED = EB.

Step2: Relate ED and BD

Since BD = BE + ED and BE = ED, then BD = ED + ED = 2ED → $\frac{1}{2}(BD) = ED$.

Answer:

The option with $\frac{1}{2}(ED)=BD$ is incorrect (note: likely a typo, should be $\frac{1}{2}(BD)=ED$ which matches the property). Assuming the option is $\frac{1}{2}(BD)=ED$, that is the correct one.

(Note: If the options are as listed, the correct property implies BD = 2ED, so the option "2(ED)=BD" is correct. The blue circle in the image likely marks this as the answer.)