NCERT Class 7 Maths Chapter 5
Parallel and Intersecting Lines
This chapter from Ganita Prakash Part 1 introduces CBSE Class 7 students to the properties of parallel and intersecting lines and the angles formed when a transversal cuts them. Students explore concepts like corresponding angles, alternate interior angles, co-interior angles, and vertically opposite angles, and apply these to solve problems involving unknown angles in geometric figures.
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Key Terms
- Parallel Lines
- Two or more lines in the same plane that never meet and remain the same distance apart at every point. They are denoted by the symbol ||.
- Transversal
- A line that intersects two or more lines at distinct points. When a transversal crosses parallel lines, it creates pairs of angles with special properties.
- Corresponding Angles
- Pairs of angles formed when a transversal crosses two parallel lines, positioned on the same side of the transversal and the same side of each parallel line. Corresponding angles are equal.
- Alternate Interior Angles
- Pairs of angles formed on opposite sides of the transversal, between the two parallel lines. When lines are parallel, alternate interior angles are equal.
- Co-interior Angles
- Pairs of angles on the same side of the transversal, between the two parallel lines, also called consecutive interior angles. They are supplementary (add up to 180°) when lines are parallel.
- Vertically Opposite Angles
- Pairs of equal angles formed directly across from each other at the point where two lines intersect. They are always equal regardless of whether the lines are parallel.
Frequently Asked Questions
What are parallel lines and how are they identified?▾
Parallel lines are lines in the same plane that never intersect and are equidistant from each other. They are identified by the || symbol. On a transversal, parallel lines create corresponding angles and alternate interior angles that are equal.
What are corresponding angles and are they equal?▾
Corresponding angles are formed when a transversal crosses two lines. They occupy the same position at each intersection — for example, both above and to the right of the transversal. When the two lines are parallel, corresponding angles are always equal.
What is the sum of co-interior angles when lines are parallel?▾
Co-interior angles (also called same-side interior angles or consecutive interior angles) are formed on the same side of the transversal between two parallel lines. Their sum is always 180° (they are supplementary).
What are vertically opposite angles?▾
When two lines cross each other, they form two pairs of vertically opposite angles at the point of intersection. Vertically opposite angles are always equal. For example, if one angle is 65°, the angle directly opposite it is also 65°.
How are alternate interior angles used to prove lines are parallel?▾
If a transversal cuts two lines and the alternate interior angles are found to be equal, then the two lines must be parallel. This property works in reverse: if lines are parallel, alternate interior angles are guaranteed to be equal.
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