Problem Analysis:
The worksheet focuses on identifying and naming points, rays, line segments, and lines based on a given geometric figure. Let's solve each part step by step.
#### Given Figure:
The figure shows several points labeled as \( P, Q, R, S, T, U \). There are also rays, line segments, and lines formed by these points.
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Solution:
#### i. Write the name in any two rays.
A
ray is defined as a part of a line that has one endpoint and extends infinitely in one direction. In the figure, we can identify the following rays:
- Ray \( \overrightarrow{QU} \)
- Ray \( \overrightarrow{QT} \)
- Ray \( \overrightarrow{QS} \)
- Ray \( \overrightarrow{QP} \)
Any two of these can be chosen. For example:
-
Answer: \( \overrightarrow{QU} \) and \( \overrightarrow{QT} \)
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#### ii. Write the name in all points.
The points in the figure are explicitly labeled. They are:
- \( P \)
- \( Q \)
- \( R \)
- \( S \)
- \( T \)
- \( U \)
Answer: \( P, Q, R, S, T, U \)
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#### iii. Write any two line segment names.
A
line segment is a part of a line with two endpoints. From the figure, we can identify the following line segments:
- Line segment \( \overline{PQ} \)
- Line segment \( \overline{QR} \)
- Line segment \( \overline{QU} \)
- Line segment \( \overline{QT} \)
- Line segment \( \overline{QS} \)
Any two of these can be chosen. For example:
-
Answer: \( \overline{PQ} \) and \( \overline{QR} \)
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#### iv. What is called \( QU \)?
In the figure, \( QU \) is shown as a straight path starting from point \( Q \) and extending indefinitely through point \( U \). This matches the definition of a
ray.
Answer: \( QU \) is called a ray, specifically \( \overrightarrow{QU} \).
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#### v. What is called \( Q \)?
Point \( Q \) is a single location in the plane. It is simply a
point.
Answer: \( Q \) is called a point.
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Final Answers:
1.
Two rays: \( \overrightarrow{QU} \) and \( \overrightarrow{QT} \)
2.
All points: \( P, Q, R, S, T, U \)
3.
Two line segments: \( \overline{PQ} \) and \( \overline{QR} \)
4.
What is \( QU \): A ray (\( \overrightarrow{QU} \))
5.
What is \( Q \): A point
Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{i. } \overrightarrow{QU} \text{ and } \overrightarrow{QT} \\
\text{ii. } P, Q, R, S, T, U \\
\text{iii. } \overline{PQ} \text{ and } \overline{QR} \\
\text{iv. } \overrightarrow{QU} \\
\text{v. } \text{A point}
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of lines segments and rays worksheet.
