RD Sharma Solutions Class 6 Maths Chapter 15 - Pair of Lines and Transversal - Free PDF Download
FAQs on RD Sharma Class 6 Maths Solutions Chapter 15 - Pair of Lines and Transversal
1. How are the properties of parallel lines and a transversal used to solve problems in RD Sharma Class 6 Maths Chapter 15?
The solutions for RD Sharma Chapter 15 rely on the specific relationships that form when a transversal intersects two parallel lines. To solve problems, you use these key properties to set up equations:
Corresponding angles are equal.
Alternate interior angles are equal.
Alternate exterior angles are equal.
Interior angles on the same side of the transversal are supplementary (add up to 180°).
By identifying the relationship between a known angle and an unknown angle, you can find the value of the unknown one.
2. What is the step-by-step method to find an unknown angle in a diagram using the RD Sharma solutions approach?
To find an unknown angle in Chapter 15 problems, the RD Sharma solutions typically follow these steps:
Identify the given lines and transversal. First, confirm if the lines are parallel.
Recognise the relationship between the known angle and the unknown angle (e.g., are they corresponding, alternate interior, etc.).
Apply the correct property. If they are alternate interior angles, set them as equal. If they are consecutive interior angles, their sum is 180°.
Form an equation and solve for the unknown variable.
3. How can you correctly identify different angle pairs like corresponding and alternate interior angles in complex diagrams?
A simple way to identify angle pairs is to look for visual cues:
Corresponding Angles: Look for an 'F' shape (forwards or backwards). The angles inside the two 'corners' of the F are corresponding.
Alternate Interior Angles: Look for a 'Z' shape (forwards or backwards). The angles within the two 'corners' of the Z are alternate interior angles.
Consecutive Interior Angles: Look for a 'C' or 'U' shape. The angles inside the shape are consecutive interior angles.
Practising with these shapes helps in quickly identifying relationships in any diagram from this chapter.
4. Why is it crucial to first confirm that lines are parallel before applying angle equality rules?
It is crucial because the special properties—such as alternate interior angles being equal or corresponding angles being equal—are only true if the two lines intersected by the transversal are parallel. If the lines are not parallel, these angle pairs still exist, but they will not be equal or supplementary. Applying these rules to non-parallel lines is a common error and will lead to incorrect solutions.
5. How can you use the concepts from Chapter 15 to prove that two given lines are parallel?
You can prove two lines are parallel by using the converse of the angle properties. If a transversal intersects two lines such that any of the following conditions is met, the lines are parallel:
A pair of corresponding angles is equal.
A pair of alternate interior angles is equal.
A pair of interior angles on the same side of the transversal is supplementary (their sum is 180°).
This reverse logic is a key problem-solving technique in geometry.
6. How do the RD Sharma solutions for Chapter 15 help with worksheet problems?
The RD Sharma solutions for Class 6 Chapter 15 provide detailed, step-by-step explanations for every type of problem involving lines and transversals. By studying these solutions, you learn the precise method to identify angle relationships, set up equations, and solve for unknown values. This foundation makes it easier to tackle similar problems in worksheets, class tests, and exams with confidence.
7. What is a common mistake when dealing with interior angles on the same side of the transversal?
A very common mistake is to assume that the interior angles on the same side of the transversal are equal. They are not. The correct property for parallel lines is that these angles are supplementary, meaning their sum is 180°. Forgetting this distinction and setting them as equal is a frequent error that leads to wrong answers in exercises.
8. Can a transversal be perpendicular to two parallel lines? How does this affect the angles formed?
Yes, a transversal can be perpendicular to two parallel lines. If a transversal is perpendicular (forms a 90° angle) to one of the parallel lines, it must also be perpendicular to the other. In this special case, all eight angles formed at the intersections are right angles (90°). This simplifies problems significantly, as all corresponding, alternate interior, and vertically opposite angles are equal to 90°.
