Grade 4 Maths Resources (8.1 Geometry - Revising Different Types ... - Free Printable

Problem Analysis:

The worksheet involves analyzing a geometric figure and answering questions about lines, angles, parallelism, and perpendicularity. Let's solve each question step by step.

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Figure Description:

The figure shows several lines intersecting at various points. Key observations:
- There are labeled points: \( A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z \).
- Lines are drawn in different orientations, some parallel, some perpendicular, and some intersecting.
- The point of intersection is marked as \( O \).

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Solutions to the Questions:

#### 1. What is the intersecting point of \( \overleftrightarrow{AB} \) and \( \overleftrightarrow{RS} \)?
- From the figure, \( \overleftrightarrow{AB} \) and \( \overleftrightarrow{RS} \) intersect at point \( O \).
- Answer: \( O \)

#### 2. Write two pairs of parallel lines and perpendicular lines in the above figure.
- Parallel Lines:
- \( \overleftrightarrow{CD} \parallel \overleftrightarrow{XY} \)
- \( \overleftrightarrow{EF} \parallel \overleftrightarrow{GH} \)
- Perpendicular Lines:
- \( \overleftrightarrow{AB} \perp \overleftrightarrow{CD} \)
- \( \overleftrightarrow{EF} \perp \overleftrightarrow{GH} \)
- Answer:
- Parallel Lines: \( \overleftrightarrow{CD} \parallel \overleftrightarrow{XY} \), \( \overleftrightarrow{EF} \parallel \overleftrightarrow{GH} \)
- Perpendicular Lines: \( \overleftrightarrow{AB} \perp \overleftrightarrow{CD} \), \( \overleftrightarrow{EF} \perp \overleftrightarrow{GH} \)

#### 3. Is there any line parallel to \( \overleftrightarrow{AB} \)?
- From the figure, there is no line explicitly shown to be parallel to \( \overleftrightarrow{AB} \).
- Answer: No

#### 4. Name the lines that are perpendicular to \( \overleftrightarrow{EF} \).
- From the figure, \( \overleftrightarrow{GH} \) is perpendicular to \( \overleftrightarrow{EF} \).
- Answer: \( \overleftrightarrow{GH} \)

#### 5. Is line \( \overleftrightarrow{CD} \) perpendicular to any line?
- From the figure, \( \overleftrightarrow{CD} \) is perpendicular to \( \overleftrightarrow{AB} \).
- Answer: Yes, \( \overleftrightarrow{CD} \) is perpendicular to \( \overleftrightarrow{AB} \).

#### 6. Name all the lines that line \( PR \) is intersecting.
- From the figure, line \( PR \) intersects the following lines:
- \( \overleftrightarrow{AB} \)
- \( \overleftrightarrow{CD} \)
- \( \overleftrightarrow{EF} \)
- \( \overleftrightarrow{GH} \)
- Answer: \( \overleftrightarrow{AB}, \overleftrightarrow{CD}, \overleftrightarrow{EF}, \overleftrightarrow{GH} \)

#### 7. Is \( \overleftrightarrow{AB} \) perpendicular to \( \overleftrightarrow{PR} \)?
- From the figure, \( \overleftrightarrow{AB} \) is not perpendicular to \( \overleftrightarrow{PR} \). They intersect at an angle other than 90 degrees.
- Answer: No

#### 8. Are lines \( \overleftrightarrow{GH} \) and \( \overleftrightarrow{XY} \) perpendicular to any other line other than \( \overleftrightarrow{CD} \)?
- From the figure:
- \( \overleftrightarrow{GH} \) is perpendicular to \( \overleftrightarrow{EF} \).
- \( \overleftrightarrow{XY} \) is not perpendicular to any other line except \( \overleftrightarrow{CD} \).
- Answer: Yes, \( \overleftrightarrow{GH} \) is perpendicular to \( \overleftrightarrow{EF} \).

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Final Answers:

1. \( O \)
2. Parallel Lines: \( \overleftrightarrow{CD} \parallel \overleftrightarrow{XY} \), \( \overleftrightarrow{EF} \parallel \overleftrightarrow{GH} \); Perpendicular Lines: \( \overleftrightarrow{AB} \perp \overleftrightarrow{CD} \), \( \overleftrightarrow{EF} \perp \overleftrightarrow{GH} \)
3. No
4. \( \overleftrightarrow{GH} \)
5. Yes
6. \( \overleftrightarrow{AB}, \overleftrightarrow{CD}, \overleftrightarrow{EF}, \overleftrightarrow{GH} \)
7. No
8. Yes, \( \overleftrightarrow{GH} \) is perpendicular to \( \overleftrightarrow{EF} \).

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Boxed Final Answer:

\[
\boxed{
\begin{array}{l}
1. O \\
2. \text{Parallel: } \overleftrightarrow{CD} \parallel \overleftrightarrow{XY}, \overleftrightarrow{EF} \parallel \overleftrightarrow{GH}; \text{ Perpendicular: } \overleftrightarrow{AB} \perp \overleftrightarrow{CD}, \overleftrightarrow{EF} \perp \overleftrightarrow{GH} \\
3. \text{No} \\
4. \overleftrightarrow{GH} \\
5. \text{Yes} \\
6. \overleftrightarrow{AB}, \overleftrightarrow{CD}, \overleftrightarrow{EF}, \overleftrightarrow{GH} \\
7. \text{No} \\
8. \text{Yes, } \overleftrightarrow{GH} \text{ is perpendicular to } \overleftrightarrow{EF}.
\end{array}
}
\]