Question

Based on the construction shown in the diagram, complete the statements with the correct symbol.
(1 point)
AM
BM
AB
CD

Answer 1

• The construction of a perpendicular bisector divides the initial segment into two equal and congruent pieces.
• The construction of a perpendicular bisector creates 90°
angles.

Answer 2

To accurately complete the statements with the correct symbols for segments **AM**, **BM**, **AB**, and **CD**, it's necessary to have an understanding of the relationships between the segments based on their lengths or positions, which would typically be indicated in a diagram.

Since I can't see the diagram you are referring to, please provide information or the relationships you would like to know about these segments. For example, if **M** is a midpoint of **AB**, then you could state that **AM = BM**, and if we know the lengths or relationships of any of the segments, we can use the appropriate symbols (like =, <, >) accordingly.

Answer 3

Based on the information provided about the construction of a perpendicular bisector, here's how you can complete the statements with the correct symbols:

1. Since a perpendicular bisector divides the segment into two equal and congruent pieces, we have:
\[
AM = BM
\]
This indicates that segment **AM** is equal in length to segment **BM**.

2. The segments created (in this case **AB** which is the whole segment being bisected), the relationship would be represented as:
\[
AB = AM + BM
\]
Since **AM** and **BM** are equal, we can express it as:
\[
AB = 2AM \quad (\text{or equivalently, } AB = 2BM)
\]

3. Since the construction of a perpendicular bisector creates 90° angles, we state that:
\[
\angle AMC = 90^\circ \quad \text{and} \quad \angle BMC = 90^\circ
\]

4. If **CD** is a segment that is also defined in some relationship with **AB**, please clarify its relationship so that I can provide the correct symbol or statement for it.

In summary:
- **AM = BM** (because the perpendicular bisector divides the segment into two equal pieces)
- **AB = AM + BM** (which could also be characterized, depending on their lengths)
- **The angles formed are right angles (90°)**

If you provide more details regarding **CD**, I can include it as well!