RS Aggarwal Solutions Class 8 Chapter-16 Parallelograms (Ex 16A) Exercise 16.1 - Free PDF
FAQs on RS Aggarwal Solutions Class 8 Chapter-16 Parallelograms (Ex 16A) Exercise 16.1
1. How do I solve for the unknown angles of a parallelogram if one angle is given, as in RS Aggarwal Class 8 Chapter 16?
To solve for the angles of a parallelogram when one angle is known, you must use two key properties:
- Opposite angles are equal: The angle directly opposite the given angle will have the same measure.
- Consecutive angles are supplementary: The angles adjacent (next to) the given angle add up to 180°.
2. What is the correct method to find the measure of all angles in a parallelogram when the adjacent angles are in a specific ratio (e.g., 4:5) in Ex 16A?
The correct method involves these steps:
- Represent the angles: Let the adjacent angles be 4x and 5x based on the ratio.
- Use the supplementary property: Since adjacent angles in a parallelogram are supplementary, their sum is 180°. Set up the equation: 4x + 5x = 180°.
- Solve for x: Combine the terms (9x = 180°) and solve for x (x = 20°).
- Calculate the angles: Substitute the value of x back into your expressions. The angles would be 4 * 20° = 80° and 5 * 20° = 100°.
- Find the remaining angles: The other two angles are opposite to these, so they will also be 80° and 100°.
3. Why must we use the property that consecutive angles are supplementary to solve problems in a parallelogram, instead of just using the sum of all angles (360°)?
While the sum of all interior angles in a parallelogram is indeed 360°, using the property that consecutive angles are supplementary (add up to 180°) is a more direct and efficient method. It allows you to create a simpler equation with fewer variables. For example, knowing just one angle (let's say ∠A) immediately allows you to find its neighbours (∠B and ∠D) using the 180° rule, which is a faster approach than setting up an equation with all four angles.
4. How does the property that 'diagonals of a parallelogram bisect each other' help in solving problems in RS Aggarwal Chapter 16?
This property is crucial for problems involving lengths. 'Diagonals bisect each other' means they cut each other into two equal halves at their point of intersection. If the diagonals are AC and BD intersecting at O, then:
- The length of segment AO equals the length of segment OC.
- The length of segment BO equals the length of segment OD.
5. What is the step-by-step approach to find the side lengths if the perimeter and the difference between adjacent sides of a parallelogram are given?
Follow this approach for accurate solutions:
- Define variables: Let the adjacent sides be 'a' and 'b'.
- Set up equations: Create two equations based on the given information. For example, 'a = b + 5 cm' and 'Perimeter = 2(a + b)'.
- Substitute and solve: Substitute the first equation into the perimeter formula. For a perimeter of 50 cm, this would be 50 = 2((b + 5) + b).
- Calculate one side: Solve the equation for 'b'. (50 = 2(2b + 5) => 25 = 2b + 5 => 20 = 2b => b = 10 cm).
- Find the other side: Use the value of 'b' to find 'a' (a = 10 + 5 = 15 cm). The sides are 10 cm and 15 cm.
6. Can I assume the diagonals of a parallelogram are equal when solving problems in Ex 16A? Why or why not?
No, you cannot assume the diagonals of a general parallelogram are equal. This is a common misconception. The property of equal diagonals only applies to special types of parallelograms, namely rectangles and squares. For a standard parallelogram, the diagonals are unequal in length unless specified otherwise. The only universal property for its diagonals is that they bisect each other.
7. Where can I find reliable, step-by-step solutions for all questions in RS Aggarwal Class 8 Maths Chapter 16, Ex 16A?
Vedantu provides detailed, step-by-step solutions for every problem in RS Aggarwal Class 8 Maths Chapter 16 (Parallelograms), Exercise 16A. Our solutions are prepared by subject matter experts and are fully aligned with the latest CBSE guidelines for the 2025-26 academic year, ensuring you learn the correct methods and properties to solve each question accurately.
