CBSE Class 7 Mathematics Chapter 10: Practical Geometry NCERT Solutions
This chapter, Practical Geometry, for CBSE Class 7 Mathematics focuses on the fundamental concepts of constructing geometric figures using a ruler and compasses. The NCERT Solutions provide step-by-step guidance for drawing parallel lines, perpendicular lines, and understanding the properties of shapes formed by these constructions. Key exercises involve drawing a line parallel to a given line through an external point, and constructing parallel lines using perpendiculars. The solutions also explore the properties of parallelograms formed through specific geometric constructions. These detailed explanations and clear construction steps are designed to help students grasp the practical aspects of geometry, build confidence in their drawing abilities, and prepare effectively for their examinations by reinforcing theoretical knowledge with practical application.
Quick info
| Board | CBSE |
|---|---|
| Class | Class 7 |
| Subject | Mathematics |
| Session | 2026 |
| Language | English |
| Type | NCERT Solutions |
| Chapter | Chapter 10 |
Chapter summary
Chapter 10, Practical Geometry, for Class 7 Mathematics NCERT Solutions covers the essential techniques for constructing geometric figures. It focuses on drawing parallel lines using ruler and compasses, constructing lines parallel to a given line through an external point, and understanding the properties of shapes formed, such as parallelograms. The solutions provide clear, step-by-step instructions for each construction, ensuring students can accurately replicate the figures and understand the underlying geometric principles.
Learning outcomes
- Understand the process of constructing parallel lines using a ruler and compasses.
- Learn to draw a line parallel to a given line through an external point.
- Construct parallel lines using perpendicular lines.
- Identify and understand the properties of geometric shapes formed by parallel lines, such as parallelograms.
Topics covered
Paper topics
- Introduction to Practical Geometry
- Construction of Parallel Lines
- Using Ruler and Compasses
- Construction through an External Point
- Construction using Perpendiculars
- Identifying Geometric Shapes
- Properties of Parallelograms
Important topics
- Constructing a line parallel to a given line
- Constructing parallel lines using perpendiculars
- Understanding the formation of parallelograms
- Precise use of ruler and compasses
PDF preview
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Questions and Solutions
Question 1
Objective: To construct a line parallel to a given line (AB) passing through an external point (C) using only a ruler and compasses.
Steps of Construction:
- Draw a line segment AB and mark a point C that is not on the line AB.
- Choose any point D on the line AB and draw a line segment connecting C to D. This segment CD acts as a transversal.
- Place the compass point on D and set a convenient radius. Draw an arc that intersects AB at point E and CD at point F.
- Without changing the compass radius, place the compass point on C. Draw an arc (let's call it GH) that intersects the line segment CD at point I.
- Now, adjust the compass to the distance EF (the length of the arc segment on AB). Place the compass point on I and draw an arc that intersects the arc GH at point J.
- Join point C to point J with a ruler and extend this line to form a line l.
The line l drawn through C is parallel to the line AB. This construction is based on the property that when a transversal intersects two lines such that the corresponding angles are equal, the two lines are parallel.
Question 2
Objective: To construct a line m parallel to a given line l, with a specific distance of 4 cm between them, using perpendiculars.
Steps of Construction:
- Draw a line l.
- Choose any point P on the line l.
- Construct a line n perpendicular to line l at point P. This line n will pass through P.
- On the perpendicular line n, measure a distance of 4 cm from point P and mark this point as X. So, PX = 4 cm.
- At point X, construct another line m perpendicular to the line n.
The line m constructed is parallel to the original line l, and the perpendicular distance between them is 4 cm. This method utilizes the property that lines perpendicular to the same line are parallel to each other.
Question 3
Objective: To construct a figure using parallel lines and identify the shape formed.
Steps of Construction:
- Draw a line l and mark a point P that is not on l.
- Construct a line m through P parallel to line l. (This can be done using methods from Question 1 or 2).
- Choose any point Q on line l and join P to Q. This segment PQ is a transversal.
- Select another point R on the line m.
- Construct a line through R that is parallel to the line segment PQ. Let this new line intersect line l at point S.
Identification of the Shape:
We have constructed line m parallel to line l (so, RS is parallel to PQ). We have also constructed line RS parallel to PQ. Therefore, the figure PQRS has two pairs of parallel sides: PQ || RS and PS || QR (since PS is part of line l and QR is part of line m, and l || m).
A quadrilateral with two pairs of parallel sides is called a parallelogram.
Conclusion: The shape enclosed by the two sets of parallel lines is a parallelogram.
Common mistakes
- Incorrectly setting the compass radius for arcs.
- Not ensuring parallel lines are equidistant.
- Confusing the steps for drawing perpendiculars versus parallels.
- Inaccurate joining of points leading to distorted shapes.
Revision tips
- Practice each construction step multiple times to build muscle memory.
- Ensure your ruler and compass are used precisely for accurate drawings.
- Label all points and lines clearly as you construct them.
- Review the properties of the shapes formed (like parallelograms) after construction.
Practice MCQs
Q1. What is the primary tool used for constructing parallel lines in this chapter?
Explanation: The chapter specifically focuses on constructions using a ruler and compasses to ensure accuracy and understanding of geometric principles.
Q2. In Exercise 10.1, Question 1, what is the relationship between the constructed line and the given line AB?
Explanation: The objective of the construction is to draw a line through an external point that is parallel to the given line AB.
Q3. When constructing a line parallel to a given line using a perpendicular, what is the distance required between the two parallel lines?
Explanation: In Question 2, a specific distance (4 cm) is chosen on the perpendicular to define the location of the parallel line.
Q4. What geometric shape is formed in Question 3 when two pairs of parallel lines enclose a region?
Explanation: The construction in Question 3 results in a parallelogram, where opposite sides are parallel.
Frequently asked questions
What is the main goal of Chapter 10 in Class 7 Mathematics?
The main goal is to teach students how to construct geometric figures, specifically parallel lines, using practical tools like a ruler and compasses, and to understand the shapes formed by these constructions.
How do the NCERT Solutions help students in Chapter 10?
The solutions provide clear, step-by-step instructions for each construction, making it easier for students to follow along, practice, and understand the methods for drawing parallel lines and other geometric figures accurately.
What tools are essential for the constructions in this chapter?
The essential tools for the constructions in this chapter are a ruler (for drawing straight lines and measuring lengths) and a compass (for drawing arcs and circles).
What is the significance of drawing a line parallel to a given line?
Drawing parallel lines is a fundamental geometric skill used in various constructions, creating specific shapes like parallelograms, and understanding concepts in geometry and design.
How does Question 3 help in understanding geometric shapes?
Question 3 guides students to construct a parallelogram by drawing two pairs of parallel lines, helping them visualize and understand the properties of this specific quadrilateral.
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