Chapter 6 Constructions and Tilings (Class 7 - Latest Maths NCERT (Ganita Prakash II) Solutions)
Seeking detailed, step-by-step NCERT Solutions for Chapter 6: Constructions and Tilings? This page provides comprehensive answers and precise geometric guides for the latest Class 7 Maths curriculum. We walk you through the essential techniques of creating a Perpendicular Bisector using only a compass and an unmarked ruler, ensuring your midpoints are mathematically perfect. Our solutions also connect these modern methods to the historical wisdom of the Śulba-Sūtras, making the logic of geometric alignment easy to grasp.
Our solutions offer clear instructions for Angle Bisection and the art of Copying Angles, which are vital for constructing complex shapes. Whether you are figuring out how to draw an 8-petalled flower or modeling the Trefoil and Pointed Arches of the Red Fort, we provide the step-by-step logic required for success. You will also find detailed explanations on the internal geometry of a Regular Hexagon, demonstrating how six equilateral triangles perfectly tile around a point to complete a $360^\circ$ rotation.
In the Tiling and Tessellation section, we provide solutions for 7-piece Tangram puzzles and use clever strategies—like the black-and-white coloring method—to solve complex tiling challenges. From understanding hexagonal bee hives to the mathematical art of M.C. Escher, these resources are designed to help you verify your constructions and master the patterns of the physical world. Curated by learningspot.co, these Ganita Prakash II solutions ensure you build the precision needed for advanced geometry.
Figure It Out (Page No. 140)
Question 1. When constructing the perpendicular bisector, is it necessary to have the same radius for the arcs above and below $XY$? Explore this through construction, and then justify your answer.
[Hint 1: Any point that is of the same distance from $X$ and $Y$ lies on the perpendicular bisector. Hint 2: We can draw the whole line if any two of its points are known.]
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Question 2. Is it necessary to construct the pairs of arcs above and below $XY$? Instead, can we construct both the pairs of arcs on the same side of $XY$? Explore this through construction, and then justify your answer.
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Question 3. While constructing one pair of intersecting arcs, is it necessary that we use the same radii for both of them? Explore this through construction, and then justify your answer.
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Question 4. Recreate this design using only a ruler and compass —
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Figure It Out (Page No. 142)
Question 1. Justify why $AB$ in Fig. 6.4 is the perpendicular bisector.
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Question 2. Can you think of different methods to construct a $90^\circ$ angle at a given point on a line using a rope?
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Figure It Out (Page No. 144 - 145)
Question 1. Construct at least 4 different angles. Draw their bisectors.
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Question 2. Construct the 8-petalled figure shown in Fig. 6.5.
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Question 3. In Step 2 of angle bisection, if arcs of equal radius are drawn on the other side, as shown in the figure, will the line $OC$ still be an angle bisector? Explore this through construction, and then justify your answer.
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Question 4. What are the other angles that can be constructed using angle bisection? Can you construct $65.5^\circ$ angle?
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Question 5. Come up with a method to construct the angle bisector using a rope.
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Question 6. Construct the following figure.
How do we construct the petals so that they are of the maximum possible size within a given square?
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Figure It Out (Page No. 147)
Question 1. Construct at least 4 different angles in different orientations without taking any measurement. Make a copy of all these angles.
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Question 2. Construct the Fig. 6.6.
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Figure It Out (Page No. 148)
Question 1. Construct $4$ pairs of parallel lines in different orientations.
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Question 2. Construct the following figure.
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Figure It Out (Page No. 151)
Question 1. Use support lines in Fig. $6.11$ to construct a pointed arch. Make different arches, by changing the radius of the arcs.
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Question 2. Make your own arch designs.
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Figure It Out (Page No. 154 - 155)
Question 1. Construct the following figures:
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Question 2. Optical Illusion: Do you notice anything interesting about the following figure? How does this happen? Recreate this in your notebook.
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Question 3. Construct this figure.
[Hint: Find the angles in this figure.]
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Question 4. Draw a line $l$ and mark a point $P$ anywhere outside the line. Construct a perpendicular to the given line $l$ through $P$.
[Hint: Find a line segment on $l$ whose perpendicular bisector passes through $P$.]
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Figure It Out (Page No. 156)
Question. How can the tangram pieces be rearranged to form each of the following figures?
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Figure It Out (Page No. 160)
Question. Are the following tilings possible?
1. Region to be tiled
2. Region to be tiled
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