CBSE Class 6 > Class 6 Notes > Mathematics > RS Aggarwal Solutions: Constructions (Exercise 10C)
RS Aggarwal Solutions: Constructions (Exercise 10C)
Solution 1:
Steps of Construction:
- Draw a line-segment AB = 7 cm with the help of a ruler.
- At A, construct ∠BAX = 90°.
- At B, construct ∠ABY = 90°.
- With A as centre and radius 4 cm, draw an arc cutting AX at D.
- With B as centre and radius 4 cm, draw an arc cutting BY at C.
- Join AC, BD and DC.
Then, ABCD is the required rectangle in which AB = DC = 7 cm and AD = BC = 3 cm.
Solution 2:
Steps of Construction:
- With the help of a ruler draw a line segment AB = 5 cm.
- At A, construct ∠BAX = 90°.
- At B, construct ∠ABY = 90°.
- With A as centre and radius 5 cm, draw an arc cutting AX at D.
- With B as centre and radius 5 cm, draw an arc cutting BY at C.
- Join AC, BD and DC.
Then, ABCD is the required square in which AB = BC = CD = DA = 6 cm.
Solution 3: In a rectangle, the diagonals are equal in length and each angle is a right angle.
Steps of construction:
- Draw line segment AB = 5 cm.
- At A, construct ∠BAX = 90°.
- At B, construct ∠ABY = 90°.
- With A as centre and radius 6.5 cm, draw an arc cutting BY at C.
- With B as centre and radius 6.5 cm, draw an arc cutting AX at D.
- Join AC, BD and DC.
Then, ABCD is the required rectangle in which AB = DC = 5 cm and diag. AC = diag. BD = 6.5 cm.
Solution 4:
In a rectangle, the diagonals are equal in length and each angle is a right angle.
Steps of construction:
- Draw line segment AB = 4.5 cm.
- At A, construct ∠BAX = 90°.
- At B, construct ∠ABY = 90°.
- With A as centre and radius 5.4 cm, draw an arc cutting BY at C.
- With B as centre and radius 5.4 cm, draw an arc cutting AX at D.
- Join AC, BD and DC.
Then, ABCD is the required rectangle in which AB = DC = 4.5 cm and diag. AC = diag. BD = 5.4 cm.
Solution 5:
Steps of construction:
- Draw line segment AB = 4.5 cm.
- At A, construct ∠BAX = 90°.
- At B, construct ∠ABY = 90°.
- At A, construct ∠BAC = 30° such that AC meets BY at C.
- With A as centre and radius equal to BC, draw an arc cutting AX at D.
- Join AC, BD and DC.
Then, ABCD is the required rectangle.
The document RS Aggarwal Solutions: Constructions (Exercise 10C) is a part of the Class 6 Course Mathematics for Class 6.
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FAQs on RS Aggarwal Solutions: Constructions (Exercise 10C)
| 1. What are constructions in geometry? |  |
Ans. Constructions in geometry refer to the methods of drawing shapes, angles, and other geometric figures using only a compass and a straightedge. These constructions help in understanding the properties of geometric figures and their relationships.
| 2. What are the basic tools used for constructions? | |
Ans. The basic tools used for constructions are a compass and a straightedge. The compass is used to draw circles and arcs, while the straightedge is used to draw straight lines. These tools are essential for performing accurate geometric constructions.
| 3. How can one construct a perpendicular bisector of a line segment? | |
Ans. To construct a perpendicular bisector of a line segment, follow these steps: First, draw the line segment. Then, place the compass at one endpoint and draw arcs above and below the segment. Repeat this from the other endpoint, ensuring the arcs intersect. Finally, draw a straight line through the intersection points; this line is the perpendicular bisector.
| 4. What is the significance of constructing angles in geometry? | |
Ans. Constructing angles in geometry is significant as it helps to create precise geometric shapes and figures. It also aids in understanding the properties of angles, such as congruence and supplementary relationships, which are foundational concepts in geometry.
| 5. Can constructions be used to solve real-life problems? | |
Ans. Yes, constructions can be used to solve real-life problems, such as in architecture for designing buildings, in engineering for creating blueprints, and in various fields where precision in measurements and angles is crucial. They provide a systematic way to create accurate geometric representations that can be applied in practical scenarios.
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