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

(1 point)
AM¯¯¯¯¯¯¯¯¯

BM¯¯¯¯¯¯¯¯¯

AB¯¯¯¯¯¯¯¯

CD¯¯¯¯¯¯¯¯

Answer 1

its bm

Answer 2

Based on the construction described, we can infer the following relationships:

1. Since the intersection line CD is perpendicular to line segment AB at the midpoint M, it indicates that the two segments AM and MB are equal in length.

2. Similarly, since CD intersects AB at M and angles are formed, CD's construction suggests that it bisects the arcs equally above and below.

Given this construction:

- Segment **AM** is equal to segment **MB**, denoted as:

\( AM \cong MB \)

- The segment **AB** is the entire length of segment AM and MB, denoted as:

\( AB \cong AM + MB \)

- Since \( C \) and \( D \) are points above and below the midpoint \( M \), and \( CD \) intersects at right angles, segments **CD** can be thought of as being in relation to AM and MB.

Thus, we can summarize it like this:

1. \( AM \cong MB \)
2. \( AB \cong AM + MB \)
3. \( CD \perp AB \)

This gives you the complete statements relating the segments with their respective symbols.