NCERT Solutions Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.3

Exercise 8.3 from "Playing with Constructions" in Class 6 Maths NCERT Solutions focuses on constructing squares and rectangles. The setup and likely ideas for this exercise should be similar to Exercise 8.1 in the earlier material on basic geometric drawing, as it will help students to construct one of the basic quadrilaterals accurately with a compass and ruler.  

Students gaining an understanding and proper construction of Exercise 8.3 is important for developing healthy drawing skills and a better understanding of geometric shapes and their properties. In this scenario, students are going to do drawings of square and rectangle shapes as the final result of each construction form. In Exercise 8.3 students draw perpendicular lines and measure lengths to arrive at accurate square and rectangle drawings; squares and rectangles, as with every other quadrilateral, are the basic building blocks for learning geometry.

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.

Key Concepts of Exercise 8.3

• Construct angles of a certain measure using a compass and protractor. 
• Copy or reproduce a given angle
• Use a given angle accurately (the same measure)
• Use measuring devices like the ruler and compass
• Improve their visualization skills through hands-on practice

2.0NCERT Exercise Solutions Class 6 Maths Chapter 8 Playing with Constructions : All Exercises 

3.0NCERT 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.

4.0Key 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.