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

1. 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 $A$ and $B$
   
   Step 3: Using a ruler, mark point $P$ on the perpendicular line at $A$ such that $AP=4\mathrm{cm}$. Using a ruler, mark point Q on the perpendicular line at B such that $\mathrm{BQ}=4\mathrm{cm}$.
   
   Step 4: Join $P$ and $Q$ using a ruler. Erase the lines above $P$ and $Q$.
   
   Step 5: Using a ruler, verify that PQ is of length 6 cm . Using a protractor, verify that $\angle \mathrm{P}$ and $\angle \mathrm{Q}$ are $90^{\circ }$ each. Step 6: We have: (i) $\mathrm{AB}=\mathrm{PQ}=6\mathrm{cm}$ and $\mathrm{AP}=\mathrm{BQ}=4\mathrm{cm}$ (ii) $\angle \mathrm{A}=\angle \mathrm{B}=\angle \mathrm{Q}=\angle \mathrm{P}=90^{\circ }$. Step 7: ABQP is the required rectangle of sides 4 cm and 6 cm .
2. 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 . $A10\mathrm{cm}B$ 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 $AP=2\mathrm{cm}$. Using a ruler, mark point Q on the perpendicular at B such that $\mathrm{BQ}=2\mathrm{cm}$.
   
   Step 4: Join $P$ and $Q$ using a ruler. Erase the lines above $P$ and $Q$.
   
   Step 5: Using a ruler, verify that PQ is of length 10 cm . Using a protractor, verify that $\angle \mathrm{P}$ and $\angle \mathrm{Q}$ are $90^{\circ }$ each. Step 6: We have: (i) $\mathrm{AB}=\mathrm{PQ}=10\mathrm{cm}$ and $\mathrm{AP}=\mathrm{BQ}=2\mathrm{cm}$ (ii) $\angle \mathrm{A}=\angle \mathrm{B}=\angle \mathrm{Q}=\angle \mathrm{P}=90^{\circ }$. Step 7: ABQP is the required rectangle of sides 2 cm and 10 cm .
3. Is it possible to construct a 4 -sided figure in which-all the angles are equal to $90^{\circ }$ 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 $\mathrm{AP}=4\mathrm{cm}$. Using a ruler, mark point Q on the perpendicular at B such that $\mathrm{BQ}=2\mathrm{cm}$, 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 $\angle \mathrm{P}$ nor $\angle \mathrm{Q}$ is $90^{\circ }$. Step 6: We conclude that it is not possible to construct a 4 -sided figure in which all angles are $90^{\circ }$ 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.