Use the image to answer the question.

Question

Two arcs are bisected by line segment A B. The arcs intersect at points C above the midpoint of A B and D below the midpoint of A B. A line is drawn from point C to D through the midpoint, M, of A B forming a right angle.
Image Long DescriptionOne arc opens to the left and crosses AB to the right of the midpoint of A B. One arc opens to the right and crosses AB to the left of the midpoint of A B.

Based on the construction shown in the diagram, complete the statements with the correct symbol.

(1 point)
AM¯¯¯¯¯¯¯¯¯

BM¯¯¯¯¯¯¯¯¯

AB¯¯¯¯¯¯¯¯

CD¯¯¯¯¯¯¯¯

Answer 1

To complete the statements based on the description of the diagram, we need to analyze the relationships between the segments.

1. AM and MB: Since point M is described as the midpoint of segment AB, it divides AB into two equal segments. Therefore, we can say:

   \( AM = MB \)

2. AB and CD: The line segment CD is formed by the vertical line drawn from point C to point D, which is perpendicular to segment AB at point M. However, there is no information provided that suggests that segments AB and CD are of equal length or proportionate to each other. Thus, we don't know the relationship between AB and CD based solely on the description.

Thus:

• For the segment lengths where we know the relationship:
  \( AM = MB \) ⟹ \( = \)

• For the comparison between AB and CD, we don't know if they are equal, so we cannot use the equality symbol. We keep it as isn't specified.

So the results are as follows:

• \( AM \overset{?}{=} MB \) ⟹ \( AM = MB \)
• \( AB \overset{?}{=}\) CD, we just can't conclude that with provided information.

So the completed statements are:

1. \( AM = MB \)
2. \( AB \neq CD \) or \( AB \text{ is not necessarily } CD \).

The context does not provide a measurement to conclude \( AB = CD \).