Class 7 RS Aggarwal Chapter-14 Properties of Parallel Lines Solutions - Free PDF Download
FAQs on RS Aggarwal Class 7 Solutions Chapter-14 Properties of Parallel Lines
1. How are parallel lines defined in RS Aggarwal Class 7, Chapter 14?
In the context of Class 7 Maths, two lines in the same plane are defined as parallel if they do not intersect at any point, no matter how far they are extended in either direction. The distance between them always remains constant. The symbol used to denote parallel lines is '||'. For example, if line 'a' is parallel to line 'b', it is written as a || b.
2. What are the key angle relationships when a transversal intersects two parallel lines, as explained in RS Aggarwal Solutions?
When a transversal line intersects two parallel lines, several key angle relationships are formed, which are essential for solving problems in this chapter. The main properties are:
Corresponding Angles are equal.
Alternate Interior Angles are equal.
Alternate Exterior Angles are equal.
Consecutive Interior Angles (or allied angles) are supplementary, meaning their sum is 180°.
3. What is the step-by-step method to solve problems for an unknown angle in Exercise 14?
To find an unknown angle in problems from RS Aggarwal Chapter 14, follow this method:
First, carefully identify the pair of parallel lines and the transversal line cutting through them.
Next, determine the relationship between the known angle and the unknown angle (e.g., are they corresponding, alternate interior, etc.).
Apply the relevant property. If the angles are corresponding or alternate, set them as equal to each other. If they are consecutive interior angles, their sum is 180°.
Finally, form an equation based on the property and solve for the unknown angle or variable.
4. How can you use the angle properties from this chapter to prove that two lines are parallel?
To prove that two lines are parallel when intersected by a transversal, you must use the converse of the parallel line properties. You need to show that one of the following conditions is true:
If a pair of corresponding angles is equal, then the lines are parallel.
If a pair of alternate interior angles is equal, then the lines are parallel.
If a pair of consecutive interior angles is supplementary (adds up to 180°), then the lines are parallel.
Proving any one of these conditions is sufficient to establish that the lines are parallel.
5. What is a transversal, and why is it important for solving questions in Chapter 14?
A transversal is a line that intersects two or more other lines at distinct points. It is critically important in this chapter because it is the line that creates all the special angle pairs (like corresponding, alternate, and interior angles). The properties of these angles, which are the basis for solving every problem in the chapter, only exist when a transversal cuts across other lines.
6. What is a common mistake students make when solving problems on parallel lines?
A very common mistake is incorrectly identifying the angle pairs or applying the wrong property. For instance, students might confuse alternate interior angles (which are equal) with consecutive interior angles (which are supplementary). Another frequent error is applying these properties to lines that are not explicitly stated or proven to be parallel. Always confirm the lines are parallel before using the angle equality or supplementary rules.
7. How do concepts like 'vertically opposite angles' help in solving problems from RS Aggarwal Chapter 14?
While not a property of parallel lines themselves, concepts like vertically opposite angles and linear pairs are frequently used as intermediate steps to solve complex problems. For example, you might be given an angle that is not directly related to the one you need to find. You can use the vertically opposite angle rule to find an angle that *is* in a corresponding or alternate relationship, allowing you to then apply the parallel line properties to find the final answer.
8. What main types of problems are found in the exercises of RS Aggarwal Class 7 Chapter 14?
The exercises in this chapter primarily focus on a few key problem types:
Finding Measures: Calculating the measure of all unknown angles in a diagram where two parallel lines are cut by a transversal and one angle is given.
Solving for Variables: Finding the value of a variable, like 'x', when angles are given as algebraic expressions.
Proving Parallel Lines: Using given angle measures to check and prove whether two lines are parallel or not.
