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NCERT Solutions Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.3
Exercise 8.3 from "Playing with Constructions" explains the step-by-step construction of rectangles using a ruler and protractor. Students verify rectangle properties such as equal opposite sides and right angles, and explore quadrilaterals with four right angles but unequal sides.
ALLEN’s NCERT Solutions for Class 6 Maths Chapter 8 Exercise 8.3 help students understand geometric constructions clearly, improve accuracy with compass and ruler, and build confidence in solving construction-based problems step by step.
1.0Download NCERT Solutions of Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.3: Free PDF
Detailed NCERT Solutions for Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.3 will help students learn how to construct squares and rectangles.
2.0Key Concepts Covered in Exercise 8.3 Class 6 Maths
• Drawing rectangles with given dimensions: Constructing rectangles step by step using specified side lengths.
• Verifying right angles (90°): Ensuring that all angles in the rectangle measure exactly 90°.
• Checking equal opposite sides: Confirming that opposite sides of a rectangle are equal and parallel.
• Logical reasoning in constructions: Analysing whether certain shapes can exist based on given conditions.
• Understanding rectangle properties: Applying geometric properties to verify constructed figures.
3.0NCERT Exercise Solutions Class 6 Maths Chapter 8 Playing with Constructions : All Exercises
4.0NCERT Class 6 Chapter 8 Playing with Constructions Exercise 8.3 : Detailed Solutions
8.3 Constructing Squares And Rectangles
- Draw a rectangle with sides of length 4 cm and 6 cm . After drawing, check if it satisfies both the rectangle properties.
Sol: We shall draw a rectangle of the form shown in figure below.
Step 1: Using a ruler, draw a line AB equal to 6 cm .
Step 2: Using a protractor, draw perpendicular lines at andStep 3: Using a ruler, mark point on the perpendicular line at such that . Using a ruler, mark point Q on the perpendicular line at B such that .Step 4: Join and using a ruler. Erase the lines above and .Step 5: Using a ruler, verify that PQ is of length 6 cm . Using a protractor, verify that and are each. Step 6: We have: (i) and (ii) . Step 7: ABQP is the required rectangle of sides 4 cm and 6 cm . - Draw a rectangle of sides 2 cm and 10 cm . After drawing, check if it satisfies both the rectangle properties.
Sol. We shall draw a rectangle of the form shown figure below.
Step 1: Using a ruler, draw a line AB equal to 10 cm . Step 2: Using a protractor, draw perpendicular lines at A and B .Step 3: Using a ruler, mark point on the perpendicular at such that . Using a ruler, mark point Q on the perpendicular at B such that .Step 4: Join and using a ruler. Erase the lines above and .Step 5: Using a ruler, verify that PQ is of length 10 cm . Using a protractor, verify that and are each. Step 6: We have: (i) and (ii) . Step 7: ABQP is the required rectangle of sides 2 cm and 10 cm .
- Is it possible to construct a 4 -sided figure in which-all the angles are equal to but opposite sides are not equal?
Sol. Step 1: Using a ruler, draw a line AB equal to 6 cm , say.
Step 2: Using a protractor, draw perpendicular lines at A and B .Step 3: Using a ruler, mark point P on the perpendicular at A such that . Using a ruler, mark point Q on the perpendicular at B such that , which is not equal to AP .Step 4: In figure, the opposite sides i.e. AP and BQ are not equal. Join P and Q using a ruler. Erase the lines above P and Q .Step 5: Using a protractor, we find that neither nor is . Step 6: We conclude that it is not possible to construct a 4 -sided figure in which all angles are and opposite sides are not equal.
5.0Key Features and Benefits Class 6 Maths Chapter 8 Playing with Constructions : Exercise 8.3
- Clarity in Steps of Construction: The solutions clearly explain each construction in easy-to-understand incremental steps. This makes it easier for students to follow and reproduce each step.
- Reinforce Properties: By constructing squares and rectangles, students reinforce their understanding of the properties of squares and rectangles.
- Improve Accuracy and Precision: With the exercise and solutions students will improve their accuracy and precision in doing the drawings for the geometric constructions.
- Problem-Solving Skills: Students are learning how to problem solve to apply their theory of geometry to geometric constructions.
- Basic for Advanced Geometry: When students understand the basic constructions they will build a foundation for advanced geometry as they move into higher grade levels.
- Exam Preparation: This solution will provide students with helpful understanding in preparation for the examinations especially in practical geometry within the CBSE syllabus.