Test: Parallel and Intersecting Lines - Class 7 MCQ

When two parallel lines are intersected by a transversal, the corresponding angles are equal. 

If angle a measures 120°, then angle b can be calculated as follows:

• Angles a and b form a linear pair, which means they are supplementary.
• Supplementary angles add up to 180°.
• To find angle b, subtract angle a from 180°:
• b = 180° - 120° = 60°.

Therefore, the measure of angle b is 60°.

If the alternate interior angles formed by a transversal intersecting two lines are equal, it can be concluded that those two lines are parallel. 

Vertically opposite angles are formed when two lines intersect. These angles are opposite each other at the intersection point and are always equal, which is a key property in geometry.

Transversal is the term used for a line that intersects two or more other lines. This type of line creates various angles and can help in understanding relationships between the intersected lines.

The interior angles on the same side of a transversal that intersects two parallel lines are supplementary, meaning they add up to 180°. 

When two lines intersect perpendicularly, they create four angles. Each of these angles measures: 90°

A linear pair of angles consists of two adjacent angles whose non-common arms form a straight line, meaning their measures add up to 180°. In other words, the two angles are next to each other (adjacent) and together form a straight angle. This is the correct definition of a linear pair, so option d is correct.

The term intersecting lines refers to two lines that cross each other at one point, known as the point of intersection.

Two lines are perpendicular to each other, creating four right angles of 90° each. When one angle at the intersection is increased by 10°, the new angle becomes 100°.

The adjacent angle, which is part of a linear pair, must be calculated as follows:

• Original angle: 90°
• Increased angle: 100°
• Sum of angles in a linear pair: 180°
• New adjacent angle: 180° - 100° = 80°

Therefore, the new measure of the angle adjacent to it is 80°.

In an optical illusion, the horizontal lines seem slanted because of zigzag patterns that create a visual distraction. However, the actual relationship between the lines is as follows:

• They are parallel, but the surrounding shapes create misleading effects.

This illusion occurs because our brains interpret the zigzag patterns, altering our perception of the lines' orientation.

Parallel lines are found in various everyday objects. Here are some examples:

• The edges of a book: The front and back covers are parallel.
• The spokes of a wheel: They extend from the hub to the rim, maintaining even spacing.
• The lines on a notebook page: They run straight and parallel to help with writing.

Among these, the most common example is the lines on a notebook page, as they are designed specifically to guide writing.

When the paper is folded vertically three times, each fold creates one vertical crease.

• After 3 folds, there are 3 vertical creases.

• The paper also has 2 vertical edges.

So, the total number of vertical lines formed is:

3 creases + 2 edges = 5 vertical lines

All these vertical lines are parallel to each other because they are all in the same vertical direction.

These vertical lines are also perpendicular to the horizontal edges of the paper, because vertical and horizontal directions meet at a right angle (90°).

Therefore,

• Number of parallel lines: 5

• Number of lines perpendicular to the horizontal edges: 5

Parallel lines are defined as lines that never meet or intersect, regardless of how far they are extended. 

Exterior Angles are formed outside two lines when a transversal intersects them.

• When two lines are crossed by a transversal, angles are created at the intersection points.
• The angles that lie outside the two lines, but on opposite sides of the transversal, are called exterior angles.
• These angles are important in various geometrical proofs and applications.