Ncert Books Class 9 Maths Chapter 11 Free Download
FAQs on Ncert Books Class 9 Maths Chapter 11 Free Download
1. What are the most frequently asked types of questions from Chapter 11, Constructions, for the Class 9 Maths exam 2025-26?
For the CBSE Class 9 exam, the most important questions from Constructions typically fall into these categories:
- Constructing bisectors of line segments and angles.
- Constructing standard angles like 60°, 90°, 45°, 30°, and 22.5° using only a compass and ruler.
- Constructing a triangle given its base, a base angle, and the sum of the other two sides.
- Constructing a triangle given its base, a base angle, and the difference of the other two sides.
- Constructing a triangle given its perimeter and two base angles.
2. What are the key triangle construction problems I should practice for the CBSE Class 9 Maths exam?
To score well, you must master the three main types of triangle constructions as per the NCERT syllabus. These are considered very important for exams:
- Type 1: Given base, one base angle, and the sum of the other two sides (e.g., given BC, ∠B, and AB + AC).
- Type 2: Given base, one base angle, and the difference between the other two sides (e.g., given BC, ∠B, and AB - AC or AC - AB).
- Type 3: Given the perimeter of the triangle and both base angles (e.g., given AB + BC + CA, ∠B, and ∠C).
3. Why is writing the 'Steps of Construction' and 'Justification' important for scoring full marks in this chapter?
Writing the Steps of Construction and providing a Justification is crucial because it demonstrates your understanding of the geometric principles behind the drawing. Marks are often divided: a portion for the neat and accurate drawing, a portion for the logical steps, and a portion for the proof (justification). Skipping them, even with a perfect drawing, will likely result in a loss of marks as per CBSE evaluation guidelines.
4. Are Objective Type or MCQ questions expected from the Constructions chapter in the exam?
Yes, you can expect 1-mark MCQs or objective questions from this chapter. These questions typically don't require you to draw but test your theoretical knowledge. For example, you might be asked:
- Which angle (e.g., 40°, 75°, 90°) cannot be constructed using only a ruler and compass?
- What is the first step in constructing the perpendicular bisector of a line segment?
- Under what condition is the construction of a triangle possible given three sides?
5. How can I construct a 90° angle using only a compass and a straightedge?
A 90° angle is one of the most fundamental constructions. You can create it by first constructing a 60° and a 120° angle and then bisecting the angle between them.
- Draw a line and mark a point P on it.
- With P as the centre, draw a large arc that intersects the line.
- From the intersection point, without changing the compass width, cut the arc once to get a 60° mark and a second time to get a 120° mark.
- Using the 60° and 120° marks as centres, draw two more arcs that intersect above the line.
- Join point P to this new intersection point. This line forms a perfect 90° angle with the original line.
6. What is a common mistake students make when constructing a triangle where the difference of two sides is given?
A very common error occurs in interpreting the 'difference' condition. Students must carefully check which side is larger. For a triangle ABC with base BC, the construction differs for the cases AB - AC and AC - AB. If AB > AC, the arc for the difference is cut on the ray of the base angle. If AC > AB, the ray must be extended downwards, and the arc is cut below the base line. Misinterpreting this leads to an entirely incorrect construction.
7. What are the essential geometrical instruments required to accurately solve questions from Chapter 11?
To ensure precision and score full marks, every student must have the following instruments in their geometry box:
- A straightedge or an ungraduated ruler for drawing lines and rays.
- A good quality compass with a tight hinge to prevent slipping.
- A protractor for measuring angles (used for verification, not construction unless specified).
- A sharply pointed pencil for drawing thin, precise lines and arcs.
