RD Sharma Solutions for Class 7 Maths Chapter 17 Constructions

Geometry is one of the most interesting and practical branches of mathematics. In Class 7, Chapter 17 of RD Sharma’s Maths book introduces students to an essential part of geometry—Constructions. This chapter helps students understand how to draw different geometric shapes and angles using only a ruler and a compass. No protractors or set squares are needed! It may sound tricky at first, but with a bit of practice and the right guidance, constructions can become fun and easy.

The RD Sharma Solutions for Chapter 17 make learning this topic much simpler. The solutions break down every step of the construction in a clear and easy-to-understand manner. Whether it is drawing a line parallel to another line, bisecting an angle, or constructing triangles with given measurements, each topic is explained in detail. These step-by-step solutions are especially helpful when students find it hard to follow the instructions in the textbook. They act like a teacher, guiding the student at every stage and ensuring that nothing is confusing.

One of the best parts of this chapter is that it combines both theory and hands-on activity. Students not only learn the concepts but also get to apply them by drawing with tools. This makes learning more engaging and improves understanding. The RD Sharma Solutions make sure that students understand the “why” behind each step, not just the “how.”

Do Check: RD Sharma Solutios for Class 7 Maths

Another benefit of using RD Sharma Solutions is that they help students get ready for exams. The exercises in this chapter include various types of construction problems, some of which are often asked in school tests. By practicing these solutions, students gain confidence and learn the correct way to approach each question. These solutions also reduce the chances of making small errors that can cost marks.

In short, RD Sharma Solutions for Class 7 Maths Chapter 17: Constructions are a useful tool for mastering this chapter. They make the learning process smooth, help build strong basics in geometry, and ensure students are well-prepared for exams. With regular practice and support from these solutions, students can improve their drawing skills and enjoy the beauty of geometric constructions.

Download RD Sharma Solutions for Class 7 Maths Chapter 17 Constructions PDF Here

RD Sharma Class 7 Chapter 17 PDF includes detailed solutions, examples, and extra questions to help you master real numbers and other topics. Click here to download the RD Sharma Class 7 Chapter 17 PDF.

Access Answers to RD Sharma Solutions for Class 7 Maths Chapter 17 Constructions

In this chapter, students will learn about decimals and how to perform basic operations with them. The solutions provided here are detailed and easy to follow, helping students understand each concept thoroughly.

Question 1: Draw triangle ABC where ∠A = 120°, and AB = AC = 3 cm. Find angles ∠B and ∠C.

Answer:

Steps to draw:

1. Start by drawing a straight line AC that is 3 cm long.

2. At point A, make an angle of 120° using a protractor.

3. From point A on the new ray, mark a point B such that AB is also 3 cm.

4. Join points B and C to complete the triangle.

5. On measuring, you will find ∠B = ∠C = 30°.

Question 2: Construct triangle ABC where ∠C = 90° and AC = BC = 4 cm.

Answer:

Steps to draw:

1. Draw a line BC that measures 4 cm.

2. At point C, draw a right angle (90°).

3. From point C on the new ray, mark point A such that AC is 4 cm.

4. Join A to B to form the triangle ABC.

Question 3: Draw triangle ABC such that BC = 4 cm, AB = 3 cm, and ∠B = 45°. Also, draw a perpendicular from A to BC.

Answer:

Steps to draw:

1. Draw a line AB = 3 cm long.

2. At point B, draw an angle of 45°.

3. From B on the 45° line, measure and mark point C such that BC = 4 cm.

4. Join A and C to form triangle ABC.

5. To draw a perpendicular from A to BC, draw arcs from point A to cut line BC at two points, M and N.

6. With M and N as centres, draw arcs above or below the line BC to meet at a point E.

7. Join A and E. This is the perpendicular from A to BC, meeting BC at point D.

Question 4: Draw triangle ABC with AB = 3 cm, BC = 4 cm, and ∠B = 60°. Also, draw angle bisectors of ∠A and ∠C, meeting at point O. Find ∠COA.

Answer:

Steps to draw:

1. Draw line BC = 4 cm.

2. At point B, make an angle of 60° and draw a line.

3. On that line, mark point A such that AB = 3 cm.

4. Join A and C to complete triangle ABC.

To draw angle bisector of ∠A:

5. With A as centre, draw equal arcs to cut AB and AC at points P and Q.

6. With P and Q as centres, draw arcs to meet at point T.

7. Join A to T. This is the bisector of angle A.

To draw angle bisector of ∠C:

8. Similarly, cut equal arcs from point C to cut CB and CA at M and N.

9. With M and N as centres, draw arcs to meet at R.

10. Join C to R. This is the bisector of angle C.

11. Let angle bisectors AT and CR meet at point O.

12. Measure angle ∠COA. It will be 120°.

Question 5: Construct triangle ABC such that BC = 4 cm, ∠B = 50° and ∠C = 70°.

Answer:

Steps to draw:

1. Draw a line BC = 4 cm.

2. At point B, construct an angle of 50° and draw a ray BX.

3. At point C, construct an angle of 70° on the same side of BC and draw a ray CY.

4. Let rays BX and CY intersect at point A.

5. Triangle ABC is now formed.

Question 6: Construct triangle ABC with BC = 8 cm, ∠B = 50° and ∠A = 50°.

Answer:

Steps to draw:

1. Draw a line BC = 8 cm.

2. At point B, make an angle of 50° and draw a ray BX.

3. At point C, draw an angle of 80° (since ∠C = 180° − 50° − 50°) and draw a ray CY.

4. Let BX and CY intersect at A. Triangle ABC is now formed.

Question 7: Draw triangle PQR where ∠Q = 80°, ∠R = 55°, and QR = 4.5 cm. Also, draw the perpendicular bisector of side QR.

Answer:

Steps to draw:

1. Draw QR = 4.5 cm.

2. At point R, draw a 80° angle and at point Q draw a 55° angle. Extend both rays until they meet at point P.

3. Triangle PQR is now complete.

To draw the perpendicular bisector of QR:

4. With Q as centre and radius more than half of QR, draw arcs on both sides of QR.

5. Repeat the same from point R. Let the arcs intersect at M and N.

6. Join points M and N. Line MN is the perpendicular bisector of QR.

Question 8: Construct triangle ABC where AB = 6.4 cm, ∠A = 45° and ∠B = 60°.

Answer:

Steps to draw:

1. Draw a line AB = 6.4 cm.

2. At point A, draw an angle of 45° and draw a ray AX.

3. At point B, draw an angle of 60° on the same side of AB and draw a ray BY.

4. Let AX and BY intersect at point C. Triangle ABC is now formed.

Question 12: Construct triangle ABC where AC = 6 cm, ∠A = 90° and ∠B = 60°.

Answer:

Steps to draw:

1. Draw a line AC = 6 cm.

2. At point A, draw a 90° angle and draw a ray AY.

3. At point C, draw an angle of 30° (since ∠C = 180° − 90° − 60°) and draw a ray CX.

4. Let AY and CX intersect at point B. Triangle ABC is now formed.

Question 9: Draw a right triangle PQR where the hypotenuse is 5 cm and one of the other sides is 4 cm.

Answer:

Steps to draw:

1. Draw line QR = 4 cm.

2. At point R, draw a right angle (90°) and draw ray RX.

3. With Q as centre and radius 5 cm, draw an arc cutting ray RX at P.

4. Join P to Q. Triangle PQR is now complete.

Question 10: Construct a right triangle where the hypotenuse is 4 cm and one side is 2.5 cm.

Answer:

Steps to draw:

1. Draw line QR = 2.5 cm.

2. At point R, draw a 90° angle and draw ray RX.

3. With Q as centre and radius 4 cm, draw an arc that cuts ray RX at point P.

4. Join P to Q. Triangle PQR is now ready.

Question 11: Construct a right triangle ABC with hypotenuse 5.4 cm and one angle of 30°.

Answer:

Steps to draw:

1. Draw line BC = 5.4 cm.

2. At point C, draw a 30° angle and draw ray CX.

3. At point B, draw a 60° angle (as other angle in right triangle) and draw ray BY.

4. Let CX and BY meet at point A. Triangle ABC is now formed.

Question 12: Draw a right triangle ABC where AB = 5.8 cm, BC = 4.5 cm and ∠C = 90°.

Answer:

Steps to draw:

1. Draw BC = 4.5 cm.

2. At point C, draw a 90° angle and draw ray CX.

3. With B as centre and radius 5.8 cm, draw an arc cutting ray CX at point A.

4. Join A to B. Triangle ABC is now complete.

Question 13: Draw a right triangle ABC with ∠C = 90°, AB = 5.2 cm, and BC = 4.6 cm.

Answer:

Steps to draw:

1. Draw BC = 4.6 cm.

2. At point C, draw a right angle and extend a ray.

3. With B as centre and radius 5.2 cm, draw an arc to intersect the ray at point A.

4. Join A to B. Triangle ABC is now complete.