Class 7 Maths Ganita Prakash Part 1 Chapter 5 MCQs – Parallel and Intersecting Lines

Two distinct straight lines can meet at one point.
If two lines shared two different points, they would lie along the same straight line. Therefore, distinct intersecting lines have exactly one common point.

Each line passes through the intersection and continues in two opposite directions.
The four rays divide the space around the point into four angles. These angles together make a complete turn of 360°.

Angles in a linear pair add up to a straight angle.
Other angle = 180° − 120°
= 60°
The two angles share one arm, and their other arms point in opposite directions along one straight line.

Vertically opposite angles are equal.
The adjacent angle = 180° − 120° = 60°.
The angle opposite the original angle = 180° − 60° = 120°.
Thus, the opposite angle has the same measure as the original angle.

The angles a and c are separated by b on one side and d on the other side. They face each other across the intersection.
Therefore, a and c are vertically opposite, while neighbouring angles form linear pairs.

Angles around the intersection add up to 360°.
Each equal angle = 360° ÷ 4 = 90°.
Therefore, all four angles are right angles, and the two intersecting lines are perpendicular to each other.

The vertically opposite angle is also 90°.
Each adjacent angle = 180° − 90° = 90°.
So all four angles measure 90°. A single right angle at the intersection is enough to establish that the lines are perpendicular.

Parallel lines lie in the same plane and remain separate however far they are extended in either direction.
Their direction can be horizontal, vertical or slanting. Being horizontal is not a necessary condition for parallelism.

Opposite edges of the square run in the same direction and do not meet when extended.
Adjacent edges meet at a corner of the square. Each corner measures 90°, so adjacent edges are perpendicular.

A segment is only a limited part of a line. Two segments may be separate even when their extended lines intersect outside the sheet.
Parallel lines must stay separate through all extensions in the same plane.

When two lines intersect, they form four angles at the point of intersection. Each pair of opposite angles is equal. These four angles help identify angle relationships such as vertically opposite angles and linear pairs.

When two lines cross, the angles that do not share a side but lie opposite each other are called vertically opposite angles. These angles are always equal and help in checking angle measurements in geometry.

Parallel lines do not intersect even when extended indefinitely. They remain equidistant at all points. This property is used in construction and design to ensure symmetry and alignment between structures.

A linear pair consists of two adjacent angles on a straight line. The angles together form a straight angle which measures 180°. This fact is used to find unknown angles in geometric problems.

The sheet already has two horizontal edges. One horizontal fold creates one crease between them.
Total parallel horizontal lines = 2 + 1 = 3.
The crease has the same direction as the top and bottom edges.

The number of horizontal strips doubles with each fold.
After three folds, strips = 2 × 2 × 2 = 8.
Eight strips have seven dividing creases.
Including the two outer edges gives 7 + 2 = 9 parallel horizontal lines.

Matching arrow marks identify lines belonging to the same parallel set.
A second set can use two matching arrows. These marks show a relationship between directions; they do not state that drawn segments have equal lengths.

A small square marks a right angle.
A right angle measures 90°.
Therefore, the two lines meet at 90° and are perpendicular. The square mark gives the angle information without needing a protractor measurement.

The third line acts as a transversal. Each of the two lines makes a 90° angle with it.
Their corresponding angles are equal. Therefore, the two distinct lines are parallel to each other.

When two lines intersect at right angles (90°), they are said to be perpendicular. Each of the four angles formed is 90°. This is a special case of intersecting lines used widely in geometry.

Alternate interior angles lie on opposite sides of the transversal and inside the two lines. If these angles are equal, it confirms that the lines are parallel. This is a key test of parallelism.

Perpendicular lines intersect in such a way that they create four right angles. Each of these angles measures 90°. This perpendicular relationship is a key feature in geometric constructions like squares and rectangles.

The mathematical symbol for parallel lines is ∥. For example, if line AB is parallel to line CD, we write AB ∥ CD. This notation is used in proofs and descriptions of geometric figures.

Each intersection of two lines creates four angles.
There are two separate intersections.
Total number of angles = 4 + 4 = 8.
The angles form two groups of four, one at each crossing of the transversal.

At each intersection, vertically opposite angles are equal. Therefore, four angles at one intersection have at most two different measures.
Across two intersections, the maximum is 2 + 2 = 4 distinct measures.

Corresponding angles occupy matching positions at the two intersections.
When the crossed lines are parallel, corresponding angles are equal.
Therefore, the corresponding angle = 60°. The 120° angles are the adjacent angles, not the matching corresponding angle.

Equal corresponding angles provide a test for parallel lines.
The transversal makes the same angle in matching positions with both lines. Therefore, the two lines have the parallel relationship, even if the drawing is slanting.

b = 180° − 120° = 60°.
The angle corresponding to b measures 70°.
Since 60° ≠ 70°, the corresponding angles are unequal. Therefore, the two lines crossed by the transversal are not parallel.

When a transversal intersects two lines, four alternate angles are formed—two on each side of the transversal. They help identify whether the lines are parallel based on angle equality.

Linear pairs are adjacent angles on the same line. Their measures always add up to 180°, making them supplementary. This relationship is useful in finding missing angle measures when one angle is known.

When a transversal intersects two parallel lines, the interior angles on the same side add up to 180°. This rule helps verify if two lines are parallel. For example, ∠ADC + ∠BCD = 180°. This property is a key identifier of parallel lines in geometry.

When two lines intersect, they form four angles. The opposite pairs of angles are called vertically opposite angles. These angles are always equal regardless of their measure. For instance, if ∠a = 120°, then its opposite ∠c is also 120° due to their symmetric position.

Alternate interior angles lie between the parallel lines on opposite sides of the transversal.
For parallel lines, these angles are equal.
Therefore, the alternate interior angle = 120°. It is not the adjacent angle in a linear pair.

Interior angles on the same side of a transversal add up to 180° when the lines are parallel.
Required angle = 180° − 50°
= 130°.
These angles are supplementary, rather than equal in this example.

The linear-pair partner of 135° is 180° − 135° = 45°.
At each intersection, two vertically opposite angles measure 45°.
There are two intersections, so 2 + 2 = 4 of the eight angles measure 45°.

At the first intersection, one right angle makes all four angles 90°.
Corresponding angles at the second intersection are also 90°.
All eight angles therefore have the same measure, so there is only one distinct angle measure.

Both l and m are perpendicular to t.
Taking t as a transversal, a corresponding angle on l is 90° and the matching angle on m is also 90°.
Equal corresponding angles show that l and m are parallel.

Parallel lines are lines that never intersect and stay equidistant. If two lines intersect, they meet at a point and cannot be parallel. The other options describe properties of parallel lines such as equal corresponding and alternate angles formed by a transversal.

A transversal is a line that crosses at least two other lines at different points. When it intersects two parallel lines, it forms eight angles, including corresponding, alternate and interior angles. It is a fundamental concept in understanding parallel line relationships.

When two lines intersect and all four angles formed are equal, each angle measures 90°. Such lines are called perpendicular lines. This is because the total angle around a point is 360°, and dividing it equally among four angles gives 90° each.

When a transversal intersects two parallel lines, corresponding angles are formed on the same side of the transversal and in matching corners. These angle pairs are always equal and help identify or prove that lines are parallel using geometric reasoning.

Using AB ∥ CD with transversal AD:
∠DAB = 180° − 60° = 120°.
The diagonal AC splits this angle into ∠DAC and ∠CAB.
∠CAB = 120° − 65° = 55°.

The linear pair gives:
x = 180° − 132° = 48°.
Alternate interior angles are equal for parallel lines.
Therefore, y = x = 48°. Finding the adjacent angle first gives the alternate angle at the other intersection.

The whole right angle measures 90°. The ray divides it into two adjacent angles.
Unknown angle + 65° = 90°.
Unknown angle = 90° − 65° = 25°.
Both parts together make the original right angle.

Both measurements start from the same horizontal ray. The larger angle contains the smaller angle and the gap between the rays.
Gap = 78° − 53° = 25°.
Adding the measurements would not give the angle between them.

Surrounding patterns can make parallel lines appear misleading.
A transversal gives an angle test: equal corresponding angles imply parallel lines.
This uses a geometric relationship rather than appearance, so it remains useful when the picture creates an illusion.

If a transversal intersects two lines and corresponding angles are equal, the two lines must be parallel. This is a property used to verify parallelism between lines. The equality of corresponding angles is both a necessary and sufficient condition for parallelism.

In geometry diagrams, parallel lines are indicated using arrow marks. One arrow mark per line is used for one pair. Two arrows show another distinct pair. This consistent notation visually indicates the relationship and is standard in geometric representations of parallel lines.

When a transversal intersects two lines, eight angles are formed. These include four angles at each point of intersection. The angles include corresponding, alternate interior and vertically opposite angles. These relationships help determine whether the lines intersected are parallel or not.

Linear pairs are adjacent angles formed when two lines intersect. The two angles lie on a straight line and therefore must sum up to 180°. This property helps solve for unknown angles and is used to verify measurements in geometric constructions.