CBSE Class 7 Mathematics Parallel and Intersecting Lines Worksheet Set 01

Very Short Answer Questions

Question 1. When do we say that a pair of lines drawn on a plane surface intersect each other?
Answer:
When the two lines meet each other at a point, we say they intersect; that point is called the point of intersection.

Teacher's Note:
1. Two straight lines can meet at only one point.
2. Use the words 'point of intersection'.

Question 2. What name is given to the pair of angles that lie opposite each other when two lines intersect?
Answer:
They are called vertically opposite angles, and they are always equal.

Teacher's Note:
1. They face each other across the meeting point.
2. Adding 'always equal' completes the answer.

Question 3. State the property of a linear pair of angles.
Answer:
The two angles of a linear pair are adjacent angles on a straight line, and they always add up to 180°.

Teacher's Note:
1. Linear pair = straight angle split into two.
2. Remember the word 'adjacent'.

Question 4. Two lines intersect each other and one of the angles formed measures 118°. Write the measure of the angle vertically opposite to it.
Answer:
Vertically opposite angles are equal, so the angle is 118°.

Teacher's Note:
1. No calculation is needed here.
2. Do not subtract from 180°; that gives the adjacent angle.

Question 5. Define perpendicular lines.
Answer:
Perpendicular lines are a pair of lines that intersect each other at a right angle (90°).

Teacher's Note:
1. The right angle is marked with a small square.
2. All four angles at the meeting point are 90°.

Question 6. Give one example of a pair of perpendicular lines that you can see in your classroom.
Answer:
Two adjacent edges of the blackboard meet at a corner at 90°, so they are perpendicular.

Teacher's Note:
1. Edges of a door, desk top or window also work.
2. Pick edges that meet at a corner.

Question 7. Define parallel lines.
Answer:
Parallel lines are a pair of lines that lie in the same plane and do not meet, however far they are extended at both ends.

Teacher's Note:
1. 'Same plane' is an important part of the definition.
2. They stay the same distance apart.

Question 8. Write any two examples of parallel lines that you see around you.
Answer:
(1) The two rails of a railway track. (2) The opposite edges of a ruler (or the ruled lines of a notebook page).

Teacher's Note:
1. Any two lines that stay the same distance apart will do.
2. Both lines must lie on the same flat surface.

Question 9. In a square sheet of paper, how are the adjacent edges related to each other, and how is this relationship shown in a figure?
Answer:
Adjacent edges are perpendicular (they meet at 90°). In a figure this is shown by a small square at the corner.

Teacher's Note:
1. Two parts to answer: the relation and the mark.
2. Opposite edges, in contrast, are parallel.

Question 10. What is a transversal?
Answer:
A transversal is a line that intersects a pair of other lines at two different points.

Teacher's Note:
1. It goes across both lines.
2. It creates eight angles.

Question 11. How many angles are formed when a transversal cuts a pair of lines?
Answer:
Eight angles are formed, four at each of the two points of intersection.

Teacher's Note:
1. 4 + 4 = 8.
2. Number them 1 to 8 in a figure to see this.

Question 12. In some pictures, lines that are really parallel appear slanted or curved. What are such pictures called?
Answer:
They are called parallel illusions, a type of optical illusion.

Teacher's Note:
1. The eye is fooled by shapes drawn around the lines.
2. Check by measuring, not by looking.

Question 13. Two lines intersect each other and one of the four angles formed measures 43°. Write the measures of the remaining three angles.
Answer:
Vertically opposite angle = 43°. The other two angles = 180° − 43° = 137° each.

Teacher's Note:
1. Check: 43 + 137 + 43 + 137 = 360.
2. Use vertically opposite and linear pair together.

Question 14. On measuring a linear pair with a protractor, Riya found that the two angles added up to 179°. Give one reason for this.
Answer:
It is a measurement error: the protractor may not be placed exactly on the vertex, or the drawn lines have thickness while ideal lines have none.

Teacher's Note:
1. The true sum is still 180°.
2. Measuring can only come close; reasoning is exact.

Question 15. Can two straight lines intersect each other at two different points? Give a reason for your answer.
Answer:
No. Two straight lines can meet at only one point; if they shared two points, they would be the same line.

Teacher's Note:
1. Only one straight line passes through two given points.
2. Give the reason, not just 'No'.

Question 16. A square sheet of paper is folded horizontally in half, and the folded sheet is folded horizontally in half once again. How many parallel lines are seen on the unfolded sheet?
Answer:
5 parallel lines: the two horizontal edges and the three creases.

Teacher's Note:
1. The second fold adds two new creases.
2. Count the edges as well as the creases.

Question 17. A square sheet already has some horizontal crease lines on it. A vertical fold is now made. How is this new crease related to the horizontal creases?
Answer:
The vertical crease is perpendicular to all the horizontal creases, meeting each at a right angle.

Teacher's Note:
1. Horizontal and vertical lines meet at 90°.
2. It is parallel to the vertical edges.

Question 18. State the property of corresponding angles formed when a transversal cuts a pair of parallel lines.
Answer:
When a transversal cuts a pair of parallel lines, the corresponding angles are equal.

Teacher's Note:
1. Corresponding means 'same position' at the two crossings.
2. The converse is also true.

Question 19. A transversal cuts a pair of parallel lines. If one of the angles measures 73°, write the measure of its corresponding angle.
Answer:
Corresponding angles on parallel lines are equal, so it is 73°.

Teacher's Note:
1. No subtraction needed.
2. Equal because the lines are parallel.

Question 20. Write, in brief, how a ruler and a set square are used together to draw a line parallel to a given line.
Answer:
Place one edge of the set square along the given line and hold the ruler firmly against another edge.
Slide the set square along the ruler and draw along the same edge. The new line makes the same angle with the ruler, so it is parallel to the given line.

Teacher's Note:
1. The ruler must not move.
2. Equal corresponding angles make the lines parallel.

Question 21. State the property of alternate angles formed by a transversal cutting a pair of parallel lines.
Answer:
Alternate angles formed by a transversal on a pair of parallel lines are always equal.

Teacher's Note:
1. Alternate angles lie on opposite sides of the transversal, between the lines.
2. They form a Z shape.

Question 22. A transversal cuts a pair of parallel lines. One of the interior angles measures 108°. Find the interior angle on the same side of the transversal.
Answer:
Same-side interior angles add to 180°, so the angle = 180° − 108° = 72°.

Teacher's Note:
1. Same side interior: supplementary.
2. Check: 108 + 72 = 180.

Question 23. Explain briefly why the eight angles formed by a transversal cutting a pair of lines cannot all be of different measures.
Answer:
At each crossing, the vertically opposite angles are equal, so the eight angles form four equal pairs and can show at most four different measures.

Teacher's Note:
1. Four pairs of vertically opposite angles.
2. Parallel lines reduce this to two measures.

Question 24. A friend says that two lines in a design are not parallel because they look slanted. How would you check whether the lines are really parallel?
Answer:
Draw a transversal across the two lines and measure a pair of corresponding angles. If they are equal, the lines are parallel, however they look.

Teacher's Note:
1. Our eyes can be fooled by illusions.
2. Measuring the gap at several places also works.

Question 25. A transversal cuts two lines so that a pair of corresponding angles measures 64° and 68°. Are the two lines parallel? Give a reason.
Answer:
No. For parallel lines the corresponding angles must be equal, but 64° ≠ 68°.

Teacher's Note:
1. Even a small difference means not parallel.
2. Extended far enough, the lines will meet.

Question 26. A crease t is folded perpendicular to a line l through a point A, and then a crease m is folded perpendicular to t through A. Why is m parallel to l?
Answer:
Both l and m make 90° with t. Taking t as a transversal, the corresponding angles are both 90°, so they are equal and m ∥ l.

Teacher's Note:
1. Two lines perpendicular to the same line are parallel.
2. This is the paper-folding method.

Question 27. A transversal cuts a pair of parallel lines. One of the two interior angles on the same side of the transversal is twice the other. Find both angles.
Answer:
Let the smaller angle be x. Then x + 2x = 180°, so 3x = 180° and x = 60°.
The angles are 60° and 120°.

Teacher's Note:
1. Same-side interior angles add to 180°.
2. Check: 120 is twice 60.

Question 28. Two lines intersect at a point. One of the angles formed is 40° less than the angle adjacent to it. Find both angles.
Answer:
The two adjacent angles form a linear pair. Let the smaller be x: x + (x + 40°) = 180°, so 2x = 140° and x = 70°.
The angles are 70° and 110°.

Teacher's Note:
1. Check: 110 − 70 = 40 and 70 + 110 = 180.
2. Adjacent angles at a crossing make a linear pair.

Question 29. Lines p and q are both parallel to the same line r. What can you say about lines p and q? Give a reason.
Answer:
p and q are parallel. A transversal makes equal corresponding angles with p and r, and with q and r, so it makes equal corresponding angles with p and q.

Teacher's Note:
1. Lines parallel to the same line are parallel to each other.
2. This idea is used in bend-angle problems.

Question 30. A transversal cuts a pair of parallel lines. One alternate angle measures (x + 25)° and the other measures (2x − 10)°. Find the value of x and the measure of each of these angles.
Answer:
Alternate angles are equal: x + 25 = 2x − 10, so x = 35.
Each angle = 35 + 25 = 60° (check: 2 × 35 − 10 = 60).

Teacher's Note:
1. Set the two expressions equal.
2. Substitute back into both to check.