Question
Based on the construction marks, what do you know about KO¯¯¯¯¯¯¯¯
and OL¯¯¯¯¯¯¯
?
(1 point)
Responses
KO¯¯¯¯¯¯¯¯=OL¯¯¯¯¯¯¯
Modifying above upper K upper O with bar equals Modifying above upper O upper L with bar
MN¯¯¯¯¯¯¯¯¯¯=KO¯¯¯¯¯¯¯¯+OL¯¯¯¯¯¯¯
Modifying above upper M upper N with bar equals Modifying above upper K upper O with bar plus Modifying above upper O upper L with bar
KO¯¯¯¯¯¯¯¯+OL¯¯¯¯¯¯¯=MN¯¯¯¯¯¯¯¯¯¯
Modifying above upper K upper O with bar plus Modifying above upper O upper L with bar equals Modifying above upper M upper N with bar
MO¯¯¯¯¯¯¯¯¯=KO¯¯¯¯¯¯¯¯+OL¯¯¯¯¯¯¯
and OL¯¯¯¯¯¯¯
?
(1 point)
Responses
KO¯¯¯¯¯¯¯¯=OL¯¯¯¯¯¯¯
Modifying above upper K upper O with bar equals Modifying above upper O upper L with bar
MN¯¯¯¯¯¯¯¯¯¯=KO¯¯¯¯¯¯¯¯+OL¯¯¯¯¯¯¯
Modifying above upper M upper N with bar equals Modifying above upper K upper O with bar plus Modifying above upper O upper L with bar
KO¯¯¯¯¯¯¯¯+OL¯¯¯¯¯¯¯=MN¯¯¯¯¯¯¯¯¯¯
Modifying above upper K upper O with bar plus Modifying above upper O upper L with bar equals Modifying above upper M upper N with bar
MO¯¯¯¯¯¯¯¯¯=KO¯¯¯¯¯¯¯¯+OL¯¯¯¯¯¯¯
Answers
Answered by
GPT-4o mini
Based on the construction marks and the relationships provided, we can deduce the following:
1. **Equality of Lengths**:
- The notation \( \overline{KO} = \overline{OL} \) indicates that the length of line segment \( KO \) is equal to the length of line segment \( OL \). This means that they are congruent segments.
2. **Sum of Lengths**:
- The equation \( \overline{MN} = \overline{KO} + \overline{OL} \) signifies that the length of line segment \( MN \) is the sum of the lengths of segments \( KO \) and \( OL \). Given the previous equality, we can also deduce that \( \overline{MN} = 2 \cdot \overline{KO} \) (or \( 2 \cdot \overline{OL} \), since they are the same).
3. **Connection of Segments**:
- Similarly, the notation \( \overline{MO} = \overline{KO} + \overline{OL} \) implies that the segment \( MO \) is constructed from the segments \( KO \) and \( OL \). Since \( KO = OL \), \( MO \) can also be defined as \( MO = 2 \cdot \overline{KO} \).
### Summary:
- \( \overline{KO} = \overline{OL} \): Segment \( KO \) is equal in length to segment \( OL \).
- \( \overline{MN} = \overline{KO} + \overline{OL} \) indicates \( MN \) is the length of both segments combined.
- \( \overline{MO} = \overline{KO} + \overline{OL} \): This shows how segment \( MO \) is also the sum of the two equal segments.
Thus, in conclusion, \( KO \) and \( OL \) are equal in length, and both segments contribute to the lengths of \( MN \) and \( MO \).
1. **Equality of Lengths**:
- The notation \( \overline{KO} = \overline{OL} \) indicates that the length of line segment \( KO \) is equal to the length of line segment \( OL \). This means that they are congruent segments.
2. **Sum of Lengths**:
- The equation \( \overline{MN} = \overline{KO} + \overline{OL} \) signifies that the length of line segment \( MN \) is the sum of the lengths of segments \( KO \) and \( OL \). Given the previous equality, we can also deduce that \( \overline{MN} = 2 \cdot \overline{KO} \) (or \( 2 \cdot \overline{OL} \), since they are the same).
3. **Connection of Segments**:
- Similarly, the notation \( \overline{MO} = \overline{KO} + \overline{OL} \) implies that the segment \( MO \) is constructed from the segments \( KO \) and \( OL \). Since \( KO = OL \), \( MO \) can also be defined as \( MO = 2 \cdot \overline{KO} \).
### Summary:
- \( \overline{KO} = \overline{OL} \): Segment \( KO \) is equal in length to segment \( OL \).
- \( \overline{MN} = \overline{KO} + \overline{OL} \) indicates \( MN \) is the length of both segments combined.
- \( \overline{MO} = \overline{KO} + \overline{OL} \): This shows how segment \( MO \) is also the sum of the two equal segments.
Thus, in conclusion, \( KO \) and \( OL \) are equal in length, and both segments contribute to the lengths of \( MN \) and \( MO \).
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