RS Aggarwal Solutions Class 8 Chapter-16 Parallelograms (Ex 16B) Exercise 16.2 - Free PDF
FAQs on RS Aggarwal Solutions Class 8 Chapter-16 Parallelograms (Ex 16B) Exercise 16.2
1. What specific properties of parallelograms are tested in the problems of RS Aggarwal Class 8 Maths Ex 16.2?
In RS Aggarwal Class 8 Maths Exercise 16.2, the questions primarily test your understanding of the properties of diagonals for different types of parallelograms. You will need to apply concepts such as:
The diagonals of a parallelogram bisect each other.
The diagonals of a rectangle are equal and bisect each other.
The diagonals of a rhombus bisect each other at right angles (90 degrees).
The diagonals of a square are equal and bisect each other at right angles.
Solving these problems requires correctly identifying the quadrilateral and applying the appropriate diagonal property.
2. How do you solve a problem where you need to find the angles of a parallelogram given only one angle in Ex 16.2?
To solve for all angles of a parallelogram when one angle is given, you must use two fundamental properties:
Opposite angles are equal: If you are given ∠A, then you immediately know that ∠C = ∠A.
Adjacent angles are supplementary (add up to 180°): You can find the adjacent angle, ∠B, by calculating 180° - ∠A. Once you have ∠B, you know its opposite angle, ∠D, is the same (∠D = ∠B). This step-by-step method allows you to find all four angles from a single given angle.
3. What is the correct method to prove a quadrilateral is a parallelogram using its diagonals, as required in Ex 16.2?
The most direct method to prove a quadrilateral is a parallelogram using its diagonals is to show that the diagonals bisect each other. To do this, you must demonstrate that the point where the two diagonals intersect is the midpoint of both diagonals. If the diagonals AC and BD of a quadrilateral ABCD intersect at a point O, you need to prove that AO = OC and BO = OD. If this condition is met, the quadrilateral is, by definition, a parallelogram.
4. Why is it important to know that the diagonals of a parallelogram bisect each other when solving problems in RS Aggarwal Solutions for Ex 16.2?
This property is crucial because it forms the basis for solving many problems in Exercise 16.2 without needing angle measurements. If the lengths of the diagonal segments are given as algebraic expressions, you can set the corresponding segments equal to each other (e.g., AO = OC) to form an equation and solve for an unknown variable. This allows you to find the full length of the diagonals or side lengths, which is a common question type in this exercise.
5. How is solving a problem about a rhombus different from a general parallelogram in Ex 16.2? What common mistakes should be avoided?
While a rhombus is a type of parallelogram, it has an additional key property: its diagonals bisect each other at right angles (90°). This is the main difference. For a general parallelogram, you only know the diagonals bisect each other. For a rhombus, you can apply the Pythagorean theorem to the four right-angled triangles formed by the diagonals. A common mistake is to assume the diagonals of a general parallelogram are perpendicular, which is only true for a rhombus or a square.
6. Can a quadrilateral with equal diagonals always be considered a rectangle? How does this concept apply to questions in Ex 16.2?
No, a quadrilateral with equal diagonals is not always a rectangle. For example, an isosceles trapezium can have equal diagonals but is not a parallelogram. For a quadrilateral to be a rectangle, its diagonals must be equal AND they must bisect each other. This is a common trap. In Ex 16.2, if you are asked to prove a parallelogram is a rectangle, you must prove its diagonals are equal. Merely knowing they are equal is not enough to prove it is a parallelogram in the first place.
7. Where can I find reliable, step-by-step solutions for all questions in RS Aggarwal Class 8 Maths Chapter 16, Exercise 16.2?
Vedantu provides clear, accurate, and step-by-step solutions for every question in RS Aggarwal Class 8 Maths Chapter 16, Exercise 16.2. The solutions are prepared by subject matter experts and follow the latest 2025-26 CBSE guidelines for methodology and marking. Each step is explained to help you understand the core properties of parallelograms and how to apply them correctly to score well in exams.
