NCERT Solutions Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.1

Exercise 8.1 focuses on constructing creative figures using a ruler, a compass, and a protractor. Students draw a “person” using arcs and perpendiculars, create wavy wave patterns using semicircles, and construct eye-shaped figures using compass arcs. It strengthens understanding of arcs, radii, midpoints, and symmetry through artistic geometric constructions.

The NCERT Solutions for this exercise are prepared by ALLEN experts to help students in their exam preparation. Each solution is solved thoroughly and systematically in a step by step manner to ensure the comprehension by students. The resource serves as a great aid in preparation of school assessments and competitive exams like the Olympiads.

1.0Download NCERT Solutions of Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.1: Free PDF

Download NCERT Solutions for Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.1. The solutions provided are detailed problem-solving guides and provide step-by-step explanations to aid students in completing the geometric constructions successfully.

2.0Key Concepts Covered in Exercise 8.1 Class 6 Maths

• Drawing perpendicular lines: Constructing lines that intersect at right angles to create accurate geometric structures.
• Using compass for arcs and circles: Creating arcs, semicircles, and circular shapes with a compass for geometric designs.
• Finding midpoints: Locating the exact middle of a line segment as a reference point for constructions.
• Constructing semicircles: Drawing half-circles using a compass and diameter as the base line.
• Symmetry in geometric artwork: Creating balanced figures where both halves are mirror images using geometric tools.

3.0NCERT Exercise Solutions Class 6 Maths Chapter 8 Playing with Constructions : All Exercises 

4.0NCERT Class 6 Chapter 8 Playing with Constructions Exercise 8.1 : Detailed Solutions

8.1 Artwork

(Construct)

1. A person How will you draw this?
   
   This figure has two components.
   
   You might have figured out a way of drawing the first part. For drawing the second part, see this.
   
   The challenge here is to find out where to place the tip of the compass and the radius to be taken for drawing this curve. You can fix a radius in the compass and try placing the tip of the compass in different locations to see which point works for getting the curve. Use your Estimate where to keep the tip. Construction steps: (i) Draw a line segment $\mathrm{AB}=4\mathrm{cm}$.
   
   (ii) At A and B , draw perpendicular with the help of protractor.
   
   (iii) Mark point D on perpendicular at A and B on the perpendicular at B such that $\mathrm{AD}=\mathrm{BC}$ $=4\mathrm{cm}$. Join DC.
   
   (iv) Mark a point E on DC such that $\mathrm{DE}=\mathrm{EC}=2\mathrm{cm}$. Draw a perpendicular at point E . Mark a point F on the perpendicular such that $\mathrm{EF}=3\mathrm{cm}$. Join FC .
   
   (v) With F as centre as radius equal to FC , drawn an arc from C to D . Extend FE to the arc.
   
   (vi) With $F$ as centre and radius equal to 1.5 cm draw a circle.
   
   (vii) Erase all the extra lines from the above drawn figure. The resultant figure represents the required person.
   
2. Wavy Wave method
   
   Step-by-Step Construction: (i) Draw the Central Line: Draw a straight horizontal line of length 8 cm . Label the endpoints as A and B . This is your central line AB . $\mathrm{AB}=8\mathrm{cm}$. (ii) Find the Midpoint of AB : Using the ruler, find the midpoint of line AB . Since $\mathrm{AB}=8\mathrm{cm}$, the midpoint will be at 4 cm from either endpoint A or B . Label this point as O . (iii) Set the Radius of the Compass: Set the radius of your compass to 2 cm . This radius is equal to one-forth of the length of AB (since we are drawing a half-circle). (iv) Draw the First Half Circle Above AB: Place the compass pointer at the midpoint 0 '. With the compass set to a radius of 2 cm , draw a half circle above the central line AB . The half-circle should pass through both points A and O'. This forms the first wave. (v) Draw the Second Half Circle Below AB: If you need to continue the wave, draw a second half-circle below the line AB . Place the compass pointer at 0 ", keeping the radius at 2 cm , and draw the half-circle in the opposite direction (below the line AB ).
   
3. Steps to Draw an Eye Using Only a Compass:
   
   Step 1: Take a line $AB$ of length $8.5\mathrm{cm}(4\mathrm{cm}+0.5\mathrm{cm}+4\mathrm{cm})$ as base. Take points $C$ and $D$ on AB such that $\mathrm{AC}=4\mathrm{cm}$ and $\mathrm{AD}=4.5\mathrm{cm}(4\mathrm{cm}+0.5\mathrm{cm})$.
   
   Step 2: Take points E and F on AB such that $\mathrm{AE}=2\mathrm{cm}$ and $\mathrm{FB}=2\mathrm{cm}$. E is the mid-point of $AC$ and $F$ is the mid-point of $DB$.
   
   Step 3: Take points E and F on AB such that $\mathrm{AE}=2\mathrm{cm}$ and $\mathrm{FB}=2\mathrm{cm}$. E is the mid-point of $AC$ and $F$ is the mid-point of $DB$.
   
   Step 4: Using a ruler, take points G, H, I, and J such that EG, EH, FI, and FJ are all equal to 1.5 cm . Equal distance can also be slightly less than or greater than 1.5 cm .
   
   Step 5: With the centre at G , drawn an arc from A to C of a radius equal to AG. Similarly, with the centre at H, I, and J draw arcs of radius equal to AG. Erase the extra lines as show
   
   Step 6: At points E and F, draw two black dots of big size.
   
   Step 7: Figure represents the required depiction of "Eyes".
4. What radius should be taken in the compass to get this half-circle? What should be the length of AX? Sol. We have $\mathrm{AB}=8\mathrm{cm}$. Since the "Wavy Wave" has two equal half circles, we have $\mathrm{AX}=\mathrm{XB}$. X is the mid-point of AB . $\mathrm{AX}=8/2=4\mathrm{cm}$ The length of AX is 4 cm . Let $M$ be the mid-point of $AX$. $\mathrm{AM}=\mathrm{MX}=4/2\mathrm{cm}=2\mathrm{cm}$ The center of the half circle is M . Radius of half circle $=\mathrm{AM}=2\mathrm{cm}$ The radius of the half circle is 2 cm .
5. Take a central line of a different length and try to draw the wave on it. Sol. Step 1: We start with the central line of different lengths, say, 10 cm .
   
   Step 2: Since $\frac{10}{2}=5$, using a ruler, take point $C$ on $AB$ such that $AC=5\mathrm{cm}$. $C$ is the mid-point of AB . As $5÷2=2.5$, using a ruler, take points D on AC and E on CB such that $\mathrm{AD}=2.5\mathrm{cm}$ and $\mathrm{CE}=2.5\mathrm{cm}.\mathrm{D}$ is the mid-point of AC and E is the mid-point of CB .
   
   Step 3: With centre at D , draw a half circle above the central line AB and of radius 2.5 cm . With centre at E , draw a half circle below the central line AB and of radius 2.5 cm .
   
   Step 4: Draw vertical lines in the half circles above and below the line AB .
   
   Step 5: The figure represents the required depiction of the given "Wavy Wave" with the central line of length 10 cm .
6. Try to recreate the figure where the waves are smaller than a half circle (as appearing in the neck of the figure 'A Person'). The challenge here is to get both the waves to be identical. This may be tricky! Sol. We shall draw a "Wavy Wave"
   
   Here, the waves are smaller than a half circle. Step 1. We start with the central line $AB$ of length 10 cm , say.
   
   Step 2. Since $10÷2=5$, using a ruler take a point C on AB such that $\mathrm{AC}=5\mathrm{cm}$. C is the midpoint of AB. Since $5÷2=2.5$, using a ruler, take points D on AC and E on CB such that $\mathrm{AD}=2.5\mathrm{cm}$ and CE $=2.5\mathrm{cm}$. D is the mid-point of AC and E is the mid-point of CB .
   
   Step 3. At D , draw a perpendicular line below AB , using a protractor. At E , draw a perpendicular line above AB , using a protractor.
   
   Step 4. Using a ruler, mark points F and G such that $\mathrm{DF}=1.5\mathrm{cm}$ and $\mathrm{EG}=1.5\mathrm{cm}$. Equal distance between DF and EG can also be slightly less than or greater than 1.5 cm .
   
   Step 5. Join AF and BG . With the centre at F , draw an arc from A to C of a radius equal to AF . With the centre at G , draw an arc from B to C of a radius equal to GB .
   
   Step 6. Draw vertical lines in figure. Also, erase the extra lines as shown in figure.
   
   Step 7. Figure represents the required depiction of a "Wavy Wave", where the waves are smaller than a half circle.

5.0Key Features and Benefits Class 6 Maths Chapter 8 Playing with Constructions : Exercise 8.1

• Step-by-Step Instruction: The solutions provide clear step-by-step instructions for each construction so that students can follow it easily.
• Conceptual Understanding: This will help the students to let them properly build the correctness of an understanding of geometry and construction and techniques.
• Drawing Skills: Using these solutions will allow students to practice a lot and develop their skills and accuracy with the use of geometric tools.
• Exam Preparation: These solutions have been aligned to the most recent NCERT syllabus offering and CBSE guidelines. They are also useful for exam preparation, especially to diagram questions.
• Error Reduction: By learning correct ways of construction, students will be able to avoid errors that have been learned the hard way.
• Visual Learning: This section of the solutions has charts and diagrams to assist learning and retention of material through visual learning.