A parallelogram has vertices upper A, upper B, upper C, and upper D. Opposite vertices are connected via diagonal lines that intersect at an interior point labeled upper O. The lines formed between each vertex and upper O are labeled.

Question

To prove that quadrilateral ABCD is a parallelogram, what must be the value of m?

(1 point)
Responses

11
11

18
18

36
36

15

Answer 1

To prove that quadrilateral ABCD is a parallelogram using the diagonals that intersect at point O, we can use the property that the diagonals of a parallelogram bisect each other.

This means that the lengths of segments AO and OC must be equal, and the lengths of segments BO and OD must be equal.

If \( m \) is the measurement associated with one of these segments (e.g., length of AO), we can set up the equations based on the total length of the diagonals. However, without specific values or relationships provided in the question, it isn't clear how to derive \( m \) from the options given.

If you have specific measurements or relationships regarding the segments created between the vertices and point O (like \( AO + OC \) or \( BO + OD \)), please share that information, or specify what kind of relationships are established between the segments so I can assist you in determining the correct value of \( m \) that proves ABCD is a parallelogram.