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The solutions for Chapter 17 – Constructions in RD Sharma Solutions for Class 9 Maths are explained thoroughly to help students grasp each concept with clarity. Every problem is solved step-by-step using illustrative diagrams, making it easier for learners to visualize and understand the geometric methods involved.
Designed by experienced educators, these solutions follow the latest CBSE curriculum for the 2025–26 academic session. The language used is simple and student-friendly, allowing learners to build a strong foundation in geometry while preparing effectively for their exams.
In this chapter, constructions focus on creating geometric shapes such as angles, lines, and triangles using only a ruler and compass—excluding tools like protractors. This traditional approach reflects classical methods used by Euclid for fundamental constructions, such as bisecting lines or creating angles of specific measurements. All exercises from Chapter 17 are systematically solved as per the RD Sharma Class 9 textbook, ensuring complete support for students’ academic needs.
Here are the RD Sharma Solutions Class 9 Maths Chapter 17 Construction Solutions, designed to help students prepare effectively for their exams. By referring to these solutions and practicing the problems, students can boost their confidence and improve their scores.
Construct a triangle ABC given AB = 6 cm, AC = 5 cm, and ∠A = 60°.
Solution: Draw AB = 6 cm. At A, construct ∠BAC = 60°, and cut AC = 5 cm on this ray. Join BC to complete triangle ABC.
Construct a triangle XYZ in which XY = 7 cm, YZ = 6 cm, and ∠Y = 45°.
Solution: Draw XY = 7 cm, make ∠XYZ = 45°, and cut YZ = 6 cm on the ray. Join XZ to complete the triangle.
Draw a triangle PQR such that PQ = 4 cm, QR = 5 cm, and ∠Q = 90°.
Solution: Draw QR = 5 cm, construct ∠PQR = 90°, cut PQ = 4 cm on the ray, and join PR.
Construct triangle ABC with AB = 7 cm, BC = 6 cm, and ∠C = 45°.
Solution: Begin with BC = 6 cm, construct ∠ACB = 45°, cut AB = 7 cm, and complete triangle ABC.
Construct a triangle given two sides and the included angle: AB = 5 cm, AC = 6 cm, ∠A = 90°.
Solution: Draw AB = 5 cm, construct ∠A = 90°, cut AC = 6 cm, and join BC.
Exercise 17.2 (Bisecting Angles and Lines)
Construct and bisect ∠ABC = 60°.
Solution: Draw ∠ABC = 60° using compass and bisect it using arc method.
Bisect a line segment of length 8 cm.
Solution: Draw 8 cm line, use compass from both ends to draw arcs, and join intersection to bisect.
Construct a 90° angle and then bisect it.
Solution: Construct ∠ABC = 90° and bisect it using compass to get 45°.
Construct a perpendicular bisector of line segment AB = 6.5 cm.
Solution: Use arcs from A and B and draw perpendicular bisector.
Construct a 120° angle and bisect it.
Solution: Use compass to make ∠120° and divide it into two 60° angles.
Exercise 17.3 (Perpendiculars from Points)
Draw a line and a point above it. Construct a perpendicular from the point to the line.
Solution: Use compass to draw equal arcs and create perpendicular through intersections.
From a point on a line, construct a perpendicular.
Solution: Use compass to mark equal arcs and draw perpendicular at the point.
Construct perpendicular from an external point to a line segment AB = 9 cm.
Solution: Follow standard construction of perpendicular from external point.
Construct a perpendicular bisector and locate its midpoint.
Solution: Use arcs and label midpoint from intersection.
Draw a perpendicular to a given ray at its starting point.
Solution: Use compass to construct 90° at the ray’s origin.
Exercise 17.4 (Triangle Constructions with Special Conditions)
Construct a triangle with base 5 cm, height 4 cm, and angle at base 60°.
Solution: Use base and height to create perpendicular, then angle to complete triangle.
Construct a triangle with base 6 cm, and angles 45° and 60° at base ends.
Solution: Draw base, construct both angles, and mark the vertex from their intersection.
Draw triangle PQR with PQ = 4.5 cm, ∠P = 70°, ∠Q = 60°.
Solution: Construct both angles at PQ ends and join their intersection as R.
Construct triangle ABC with AB = 5 cm, angle B = 90°, and angle C = 45°.
Solution: Use angle constructions and intersection to form triangle.
Construct triangle where ∠B = 90°, AB = 4 cm, and BC = 3 cm.
Solution: Construct right angle at B and mark points at given lengths.
Advanced Constructions (Altitude, Medians)
Construct triangle and draw altitudes from each vertex.
Draw medians of triangle ABC.
Construct angle of 30° and 60° using compass.
Bisect angle of 75°.
Draw triangle given perimeter and two angles.
Construct triangle with base and height using compass and scale.
Construct equilateral triangle using compass.
Draw 135° angle using bisection.
Construct triangle from given sides using SSS rule.
Construct triangle using ASA rule.
Construct triangle from RHS (Right angle-Hypotenuse-Side).
Construct angle of 105° using only compass.
Draw triangle with given side and angle bisector.
Draw triangle and mark incenter.
Draw triangle and construct circumcenter.
Construct triangle and draw all perpendicular bisectors.
Draw triangle and show centroid using medians.
Construct triangle and locate orthocenter.
Draw a triangle and inscribe a circle.
Draw triangle and circumscribe a circle.
1. Builds Strong Geometric Foundations
Chapter 17 of RD Sharma covers Constructions, a vital area of geometry that lays the groundwork for higher mathematical reasoning and precision. The solutions provided help students understand how to draw geometrical figures like angles, triangles, perpendiculars, and bisectors using only a ruler and compass. These fundamental skills are essential for both academic exams and real-world applications in architecture, engineering, and design.
2. Step-by-Step Visual Approach
Each question in RD Sharma’s solution is solved with clear, step-by-step instructions along with corresponding geometric figures. This visual and procedural clarity enables students to follow the logic behind each construction, helping them grasp not just the “how,” but also the “why” behind each method.
3. Aligned with CBSE Curriculum
The RD Sharma Solutions strictly follow the CBSE syllabus for the academic year 2025–26. This ensures that students are well-prepared for school exams and internal assessments without missing out on any topic mandated by the board.
4. Enhances Accuracy and Precision
Geometry demands a high level of accuracy. By practicing from these structured solutions, students develop precision in using instruments like the compass and ruler—an important skill set for mathematical drawing tasks. The solutions emphasize exact measurements, correct angles, and systematic constructions.
5. Simplifies Complex Concepts
Even complex geometrical constructions are broken down into easy-to-understand steps using simple language. This makes the topic accessible to all students, including those who may struggle with visualizing or executing geometric methods on their own.
6. Useful for Competitive Exams
Constructions are a common part of Olympiads, NTSE, and other entrance tests. Practicing RD Sharma’s solutions gives students an extra edge in competitive exam preparation by strengthening their conceptual clarity and problem-solving skills in geometry.
7. Boosts Exam Confidence
Since the solutions cover each question from the RD Sharma textbook thoroughly, students feel more confident while attempting similar problems in their exams. Regular practice also improves time management and accuracy during tests.
8. Guided by Expert Faculty
These solutions are prepared by subject matter experts who understand students’ learning curves and common errors. Their guidance through these solutions ensures a deeper understanding and correct application of geometric principles.
The solutions provide step-by-step guidance with diagrams, making it easier for students to understand and accurately perform constructions. They also help in developing visual and analytical thinking.
Chapter 17 focuses on geometric constructions using only a compass and a straightedge. Topics include constructing angles, triangles, perpendiculars, angle bisectors, and various other geometric figures without the use of a protractor.
Yes, all RD Sharma solutions are updated and aligned with the CBSE syllabus for the academic year 2025–26, ensuring relevance to school exams and board guidelines.
Yes, each solution is accompanied by clear diagrams to visually demonstrate the construction steps, improving clarity and comprehension