NCERT Solutions Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.5

In Class 6 Maths Chapter 8 - Playing with constructions, Exercise 8.5 is a formative learning exercise that allows learners to practice writing angles without a protractor, but rather with a compass and a straightedge. The angles will be of special measures (e.g., 60°; 90°; 30°; 120°), and this exercise helped establish a student's ability to understand and "see" and replicate mathematical ideas through kinesthetic learning.

Your NCERT Solutions Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.5, with expert contributions from the best educators at ALLEN, will provide simple, step-by-step solutions to each construction problem, understanding and mastering the methods, and with that the confidence of handling geometric instruments related to constructions properly and accurately.

1.0Download NCERT Solutions of Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.5: Free PDF

Download NCERT Solutions Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.5 in easy-to-access PDF format. Understand compass-based angle constructions explained clearly with level of detail practiced at Allen.

2.0Key Concepts Covered in Exercise 8.5 Class 6 Maths

• Integrated Constructions: These are constructions of line segments, angles, perpendicular lines, squares, and rectangles in a single, more complicated figure.
• Dividing Segments and Angles: Use constructions of bisecting line segments or angles to construct a given length.
• Circle-Based Constructions: may involve the use of a compass to construct circles (or arcs) with straight-line figures (may create patterns or designs).
• Symmetry and Patterns: a construction where the figures show symmetry or has repeating shapes; includes UNIFORM measurement or taping of shapes.
• Problem Solving Applications: Where constructions are used to to solve word problems, scenarios, and geometric drawings.

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

4.0NCERT Class 6 Chapter 8 Playing with Constructions Exercise 8.5 : Detailed Solutions

8.5 Exploring Diagonals Of Rectangles And Squares

1. Construct a rectangle in which one of the diagonals divides the opposite angles into $50^{\circ }$ and $40^{\circ }$. Sol. We shall draw a rectangle of the form shown in figure.
   
   Step 1: Using a ruler, draw a line AB equal to 4 cm , say.
   
   Step 2: Using a protractor, mark dots C and D at angles $50^{\circ }$ and $90^{\circ }\left(50^{\circ }+40^{\circ }\right)$, keeping the central point of the protractor at A .
   
   Step 3: Using a protractor, draw a perpendicular line to AB at B and let it intersect the extended line AC at E. Step 4: Using a protractor, draw a perpendicular line to BE at E and let it intersect the extended line AD at F.
   
   Step 5: Erase the extra lines in figure.
   
   Step 6: Above figure is the required rectangle in which one of the diagonals divides the opposite angles into $50^{\circ }$ and $40^{\circ }$.
2. Construct a rectangle in which one of the diagonals divides the opposite angles into $45^{\circ }$ and $45^{\circ }$. What do you observe about the sides? Sol. Do it yourself.
3. Construct a rectangle one of whose sides is 4 cm and the diagonal is of length 8 cm . Sol. We shall draw a rectangle of the form shown in figure below.
   
   Step 1: Using a ruler, draw a line $AB$ equal to 4 cm .
   
   Step 2: Using a protractor, draw a perpendicular line to AB at A and B .
   
   Step 3: With the centre at $A$ and a radius equal to 8 cm , draw an arc to intersect the perpendicular at B . Similarly, draw an arc of radius 8 cm with a centre at B to intersect perpendicular at A.
   
   Step 4: Join the points of intersection of arcs by PQ .
   
   Step 5: Erase the extra lines in
   
   Step 6: The required rectangle with one side equal to 4 cm and diagonals of length 8 cm .
4. Construct a rectangle one of whose sides is 3 cm and the diagonal is of length 7 cm . Sol. Do yourself.
5. Construct a bigger house in which all the sides are of length 7 cm . Recreate the given figure. Note that all the lines forming the border of the house are of length 7 cm . Sol.
   
   Step 1: Using a ruler, draw a line DE equal to 7 cm .
   
   Step 2: Using a protractor, draw perpendicular lines to DE at D and E . Take point B perpendicular at D such that BD is 7 cm . Take point C on perpendicular at E such that CE is 7 cm .
   
   Step 3: $7\mathrm{cm}-1\mathrm{cm}=6\mathrm{cm}$ and $6\mathrm{cm}÷2=3\mathrm{cm}$. Using a ruler, take points $P$ and $Q$ on $DE$ such that $\mathrm{DP}=3\mathrm{cm}$ and $\mathrm{QE}=3\mathrm{cm}$. Using a protractor, draw perpendiculars to DE at P and Q of length 2 cm each.
   
   Step 4: Join $R$ and $S$. With centres at $B$ and $C$ and a radius of 7 cm , draw arcs to intersect at point A . Join AB and AC . With the centre at A and a radius of 7 cm , draw an arc from B to C . Also, erase the extra lines.
   
   Step 5: The required recreation of the given house with all the lines forming the border of the house of length 7 cm .
6. Try to recreate 'A Person', 'Wavy Wave', and 'Eyes' from the section Artwork, using ideas involved in the 'House' construction. Sol. Do yourself.
7. Is there a 4 -sided figure in which all the sides are equal in length but are not squares? If such a figure exists, can you construct it? Sol. Step 1: Draw a line and take points $A$ and $B$ on it such that $AB=5\mathrm{cm}$, say.
   
   Step 2: Using a protractor, take points $C$ and $D$ such that angles on the right of $A$ and on the right of B are $60^{\circ }$ each.
   
   Step 3: Using a ruler, take point $P$ on $AC$ such that $AC=5\mathrm{cm}$ and $Q$ on $BD$ such that $BD=5\mathrm{cm}$. Join P and Q .
   
   Step 4: Using a ruler, we measure the distance PQ . PQ is equal to 5 cm . Thus, in figure ABQP , each side is equal to 5 cm . Here $\angle \mathrm{A}$ is $60^{\circ }$, which is not equal to $90^{\circ }$. $\therefore \mathrm{ABQP}$ is not a square. Step 5: We find that there are 4 -sided figures in which all the sides are equal in length but are not squares.

5.0Key Features and Benefits Class 6 Maths Chapter 8 Playing with Constructions : Exercise 8.5

• NCERT Solutions designed according to the Class 6 curriculum framework.
• Step-by-step construction methods that are easy for beginners to follow.
• Clear and appropriate diagrams provided for each geometric construction.
• Helps students focus on accuracy and proper use of geometric tools.
• Supports self-paced learning and helps students prepare confidently for exams.