🌈⚡Key To Enjoy Learning Maths☘🌈: 2025

Monday, July 14, 2025

Class 6 Maths – Chapter 2: Lines and Angles - Case-Based Study Questions

Class 6 Maths – Chapter 2: Lines and Angles

🎓 Case-Based Study Questions

🧾 Case Study 1: The Clock Shop

Case:
Riya visits a clock shop and observes different wall clocks showing various times. She notices the angles formed between the hour and minute hands.

Clock	Time Displayed	Observation
A	3:00	Hands form a 90° angle
B	6:00	Hands form a straight line
C	2:00	Hands form an acute angle

Questions:

What type of angle is formed in Clock A?
a) Acute
b) Obtuse
c) Right
d) Straight
✅ Answer: c) Right
What is the measure of the angle in Clock B?
a) 90°
b) 180°
c) 120°
d) 45°
✅ Answer: b) 180°
In Clock C, the angle formed is less than 90°. What type of angle is this?
✅ Answer: Acute angle
Write the name of two objects in your house that show right angles like Clock A.
✅ Answer: Examples may include corners of books, TV screens, tiles, etc.

📏 Case Study 2: The Road Intersection

Case:
Two roads cross each other near Aryan’s school. The municipal engineer says they intersect perpendicularly. Aryan sees four equal angles formed at the intersection.

Questions:

What is the measure of each angle formed?
✅ Answer: 90°
What are such angles called?
✅ Answer: Right angles
What is the relationship between the two roads?
a) Parallel
b) Intersecting
c) Perpendicular
d) Skew
✅ Answer: c) Perpendicular
How many right angles are formed when two perpendicular lines cross?
✅ Answer: 4
Draw and label two perpendicular lines using a ruler and a set square.
✅ (Student drawing question)

📐 Case Study 3: Art Class Geometry

Case:
During an art activity, Meera draws two lines that never meet, even if extended. She decorates the space between them and labels the lines as AB and CD.

Questions:

What is the relationship between line AB and line CD?
✅ Answer: Parallel lines
Can parallel lines ever intersect?
✅ Answer: No
Meera now draws a third line EF that cuts both AB and CD. What is EF called?
✅ Answer: Transversal
When a transversal cuts two parallel lines, what types of angles are formed?
✅ Answer: Corresponding, alternate interior, alternate exterior angles
Identify one real-life example of parallel lines from your surroundings.
✅ Answer: Railway tracks, lines on a ruled notebook, edge of a table

🎯 Case Study 4: Building the School Fence

Case:
While helping to install the school fence, students used measuring tapes and set squares to form corners. They ensured every corner was at a right angle.

Questions:

Why did they use a set square for the corners?
✅ Answer: To form right angles accurately
How many degrees is a right angle?
✅ Answer: 90°
If four corners of the school fence are each right angles, what shape is formed?
✅ Answer: Rectangle or square
If one corner was more than 90°, what type of angle would it be?
✅ Answer: Obtuse angle
Which tool can you use to measure any angle?
✅ Answer: Protractor

Sunday, July 13, 2025

Class: 6 Chapter: 2 LINES AND ANGLES – WORKSHEET-2 answer key

LINES AND ANGLES – ANSWER KEY

Class 6 | Chapter 2 | Total Questions: 52

📘 Topic-wise Answer Key with Explanations & Competencies

1. Understanding Points, Lines, Line Segments, and Rays

Competency: Identify and differentiate between basic geometrical figures.

Answers:
a)

Point: A point represents a location. It has no length, breadth, or thickness. Example: Dot (.)
Line: A straight path extending in both directions without end. Example: AB↔
Line Segment: A part of a line with two endpoints. Example: AB
Ray: A part of a line with one endpoint, extending endlessly in one direction. Example: AB→

b) Correct Answer: b) AB→

a) False (A line has no endpoints; it extends indefinitely.)
b) False (A point has no length.)

d) Diagrams to be drawn:

Two rays with common endpoint (O): OA→ and OB→
Two intersecting lines: Lines AB↔ and CD↔ intersecting at point P

e) Correct Answer: a) One

2. Intersecting and Parallel Lines

Competency: Visualize intersecting and parallel lines in real life.

Answers:
a) Intersecting Lines: Lines that meet at a point.
b) Parallel Lines: Lines that never meet, even if extended. Example: Railway tracks.
c) Draw 2 pairs of parallel lines: AB‖CD and EF‖GH

a) Parallel
b) Intersecting

e) Correct Answer: c) A is true, R is false

3. Angles and Their Types

Competency: Identify, classify, and measure angles.

Answers:
a) An angle is formed when two rays meet at a point (vertex).
b) Vertex: The common endpoint of two rays forming an angle.

c) Matching:

Acute angle → (ii) less than 90°
Right angle → (i) 90°
Obtuse angle → (iii) greater than 90° and less than 180°

d) Diagrams to be drawn for each angle.

a) Reflex
b) Straight

4. Pair of Angles

Competency: Understand complementary, supplementary, adjacent, and vertically opposite angles.

Answers:
a) Complementary angles: Sum = 90°. Example: 60° and 30°.
b) Supplementary angles: Sum = 180°. Example: 110° and 70°.

c) Complement of 35° = 55°
d) ∠Y = 180° - 60° = 120°
e) Adjacent angles diagram: Two angles sharing a common side.

5. Properties of Angles on a Straight Line and at a Point

Competency: Apply angle properties to solve problems.

Answers:
a) Sum on straight line = 180°
b) Vertically opposite angles are equal.

c) ∠B = 180° - 120° = 60°
d) Vertically opposite angle of 75° = 75°

e) If one angle is 50°, others are 50°, 130°, 130° (by vertically opposite and linear pair rules).

🧠 Competency-Based Questions

6. Application Questions

Competency: Apply geometry concepts in real-life contexts.

Answers:
a) Acute angle
b) Right angle
c) Supplementary angle of 89° = 91°
d) Freehand draw approximately 150°
e) Right angle (90° at 3 PM)

7. Assertion-Reasoning

Competency: Analyze statements logically.

Answers:
a) Correct Answer: c) A is false, R is true
b) Correct Answer: a) Both A and R are correct and R explains A
c) Correct Answer: a) Both A and R are correct and R explains A
d) Correct Answer: a) Both A and R are correct and R explains A

8. Case Study Based

Competency: Analyze geometrical concepts in practical situations.

Case Study 1:
a) Acute and obtuse angles.
b) Yes, vertically opposite angles are equal. Example: 50°-50°, 130°-130°
c) Typically 10 acute angles in a star.

Case Study 2:
a) Intersecting lines (diagonals), parallel lines (sides), right angles (corners).
b) Diagonals can form obtuse angles (more than 90°) inside rectangles.
c) Sum = 360°

9. Higher Order Thinking Skills (HOTS)

Competency: Apply reasoning and justify answers.

Answers:
a) Draw X and Y axis meeting at 90°.
b) No. Both obtuse angles > 90°. Their sum > 180°.
c) Example: Scissors blades, crossed roads.
d) Sum of other two angles = 90°
e) 3x + x = 180° ⇒ 4x = 180° ⇒ x = 45°

10. Mixed MCQs & Fill in the Blanks

Competency: Recall facts, apply properties.

Answers:
a) c) AB
b) Parallel
c) Complete/Full angle
d) One
e) Let one angle be x, other = 2x
x + 2x = 180° → 3x = 180° → x = 60°, 120°

Class: 6 Chapter: 2 LINES AND ANGLES – WORKSHEET-1

📝 LINES AND ANGLES – WORKSHEET

Class: 6
Chapter: 2 – Lines and Angles
Total Questions: 52
Types: Objective, Very Short Answer, Short Answer, Case-based, Assertion-Reasoning

📘 Topic-wise Question Bank

📌 1. Understanding Points, Lines, Line Segments, and Rays

Competency: Identify and differentiate between basic geometrical figures.

Define the following with examples:
a) Point
b) Line
c) Line Segment
d) Ray
Which of the following represents a ray?
a) AB↔
b) AB→
c) AB←→
d) AB
True or False:
a) A line has two endpoints.
b) A point has a definite length.
Draw a diagram to show:
a) Two rays with a common endpoint.
b) Two intersecting lines.
Multiple Choice: How many lines can be drawn through two distinct points?
a) One
b) Two
c) Infinite
d) None

📌 2. Intersecting and Parallel Lines

Competency: Visualize intersecting and parallel lines in real life.

Define intersecting lines.
Define parallel lines with a real-life example.
Draw two pairs of parallel lines and label them.
Identify whether the following pairs of lines are intersecting or parallel.
a) Railway tracks
b) Scissors blades
Assertion (A): Railway tracks are parallel lines.
Reason (R): Parallel lines meet at some point.
a) A and R are true, and R is correct explanation of A
b) A and R are true, but R is not correct explanation of A
c) A is true, R is false
d) A is false, R is true

📌 3. Angles and Their Types

Competency: Identify, classify, and measure angles.

Define an angle.
What is the vertex of an angle?
Match the following:

Acute angle → (i) 90°
Right angle → (ii) less than 90°
Obtuse angle → (iii) greater than 90° and less than 180°

Draw one angle of each type: acute, obtuse, right, straight, reflex.
Fill in the blanks:
a) An angle more than 180° but less than 360° is called a ______ angle.
b) An angle of 180° is called a ______ angle.

📌 4. Pair of Angles

Competency: Understand complementary, supplementary, adjacent, and vertically opposite angles.

Define complementary angles. Give one pair.
Define supplementary angles. Give one pair.
If ∠A = 35°, what is its complement?
If ∠X + ∠Y = 180°, and ∠X = 60°, find ∠Y.
Draw and show a pair of adjacent angles.

📌 5. Properties of Angles on a Straight Line and at a Point

Competency: Apply angle properties to solve problems.

What is the sum of angles on a straight line?
State the vertically opposite angle property.
Find the missing angle:
∠A + ∠B = 180°, ∠A = 120°.
Find the vertically opposite angle of 75°.
In a figure, if two lines intersect and one angle is 50°, find all other angles.

🧠 Competency-Based Questions

📘 6. Application Questions

Ria opens a book and notices the angle between the two pages is around 40°. What type of angle is it?
A ladder leans against a wall forming an angle of 90° with the ground. What type of angle is this?
Find the supplementary angle of 89°.
Estimate and draw an angle of approximately 150°.
The hour and minute hands of a clock at 3 PM form what kind of angle?

📘 7. Assertion-Reasoning Type

Assertion (A): Two lines can intersect at two points.
Reason (R): Lines can bend in space.
a) Both A and R are correct and R explains A
b) Both A and R are correct but R doesn’t explain A
c) A is false, R is true
d) A is true, R is false
Assertion (A): A straight angle measures 180°.
Reason (R): Straight angle lies on a straight line.
a) Both A and R are correct and R explains A
b) Both A and R are correct but R doesn’t explain A
c) A is false, R is true
d) A is true, R is false
Assertion (A): All vertically opposite angles are equal.
Reason (R): They are formed by intersecting lines.
Choose the correct option.
Assertion (A): An acute angle can never be a supplementary angle.
Reason (R): Acute angle is less than 90°.

📘 8. Case Study Based

Case Study 1:

Priya made a star using sticks. She noticed many intersecting lines and angles at the center of the star.
35. Identify at least two types of angles formed at the center.
36. Are there any vertically opposite angles? Prove with values.
37. How many acute angles can be formed in such a star?

Case Study 2:

In a classroom, the blackboard is rectangular and mounted flat on the wall. A diagonal is drawn.
38. Identify all the types of lines and angles in the figure.
39. Is the diagonal forming any right or obtuse angles? Justify.
40. Find the sum of all angles inside the rectangle.

📘 9. Higher Order Thinking Skills (HOTS)

Draw two rays that make exactly 90° angle without using a protractor.
Can two obtuse angles be supplementary? Explain with a counterexample.
Give two real-life examples where vertically opposite angles are observed.
A triangle has one right angle. What is the sum of the other two angles?
A straight line forms two adjacent angles. One is 3x and the other is x. Find x.

📘 10. Mixed MCQs & Fill in the Blanks

Which of the following is not an angle?
a) ∠A
b) 90°
c) AB
d) ∠XYZ
Lines that never meet are called ________.
An angle of 360° is called a ________ angle.
A ray has ______ endpoint(s).
Two angles are supplementary. One is twice the other. Find both.

CLASS 6 CH -1 & 2 HOME TEST JULY 2025-26

HOME TEST JULY 2025-26

Q1: The next number in the sequence: 1, 4, 9, 16, 25____ (F/B) (1Mark)

Q2. What comes next ______? (1 Mark)

Q3. Number of points in the following figure are_____ (1 Mark)

Q4. The meeting point of a pair of arms of an angle is called ______ (1 Mark)

Q5. Rihan marked one point on a piece of paper. How many different lines can he draw that pass

through the point? (1 Mark)

Q6. Write any two sequences of powers (1 Mark)

Q7. Write first four triangular numbers and show any one of them pictorially (2 Marks)

Q8. Continue the pattern for the next three terms: 1, 2, 4, 8, ___, ___, ___. (3 Marks)

Q9. . Match the items of column A in column B with their respective values (4 Marks)

COLUMN A	COLUMN B
(A) The line segment joiining points A and B is denoted by	(i) vertex
(B) Meeting point of a pair of sides is called	(ii)
(C) A Ray PQ is denoted by	(iii) Acute angle
(D) Angle measure of less than 90⁰ is called	(iv)

Saturday, July 12, 2025

ASSERTION-REASONING WORKSHEET CH-10 The Other Side of Zero CLASS 6

ASSERTION-REASONING WORKSHEET

Chapter: The Other Side of Zero (Integers) FOR DOWNLOAD PDF CLICK HERE
Class: 6 | NCERT Maths Chapter 10

✍🏽 Choose the correct option:
(A) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
(B) Both Assertion and Reason are true, but Reason is not the correct explanation.
(C) Assertion is true, but Reason is false.
(D) Assertion is false, but Reason is true.

Q1.

Assertion (A): Integers include positive numbers, negative numbers, and zero.
Reason (R): Integers are only the numbers greater than zero.
Option: ___

Q2.

Assertion (A): The opposite of +7 is −7.
Reason (R): Opposite integers are at equal distance from zero but on opposite sides.
Option: ___

Q3.

Assertion (A): Zero is a positive integer.
Reason (R): Zero lies to the right of all negative numbers on the number line.
Option: ___

Q4.

Assertion (A): −3 is smaller than −2.
Reason (R): On a number line, numbers towards the left are smaller.
Option: ___

Q5.

Assertion (A): Integers can be represented on a number line.
Reason (R): Each integer has a fixed position on the number line.
Option: ___

Q6.

Assertion (A): The sum of two negative integers is a positive integer.
Reason (R): Negative plus negative makes the number smaller.
Option: ___

Q7.

Assertion (A): Zero has no sign.
Reason (R): Zero is neither positive nor negative.
Option: ___

Q8.

Assertion (A): The opposite of 0 is 0.
Reason (R): Zero is at the center of the number line and has no direction.
Option: ___

Q9.

Assertion (A): −8 + (+3) = −5
Reason (R): Adding a positive number to a negative number shifts to the right on the number line.
Option: ___

Q10.

Assertion (A): −2 − (−3) = 1
Reason (R): Subtracting a negative number is same as adding its positive.
Option: ___

Q11.

Assertion (A): −10 is greater than −9.
Reason (R): Greater negative number means greater value.
Option: ___

Q12.

Assertion (A): (−4) + (−5) = −9
Reason (R): When two negative numbers are added, their sum is also negative.
Option: ___

Q13.

Assertion (A): Addition of two integers always results in a larger integer.
Reason (R): Adding any two numbers always increases value.
Option: ___

Q14.

Assertion (A): Integers are closed under subtraction.
Reason (R): Subtracting any two integers always gives another integer.
Option: ___

Q15.

Assertion (A): Zero is the identity for addition of integers.
Reason (R): Adding zero to any integer doesn’t change its value.
Option: ___

Q16.

Assertion (A): On the number line, the farther a negative number is from zero, the smaller it is.
Reason (R): Distance from zero increases negativity.
Option: ___

Q17.

Assertion (A): The sum of a number and its opposite is always zero.
Reason (R): Opposites cancel each other on the number line.
Option: ___

Q18.

Assertion (A): The result of subtracting a positive integer from a negative integer is always negative.
Reason (R): Subtracting a positive makes a number smaller.
Option: ___

Q19.

Assertion (A): Integers help in representing real-life situations like gains and losses.
Reason (R): Positive and negative numbers can represent profit and loss respectively.
Option: ___

Q20.

Assertion (A): −1 is the greatest negative integer.
Reason (R): On the number line, −1 is closest to zero among all negative numbers.
Option: ___
ANSWER KEY CLICK HERE

ASSERTION-REASONING WORKSHEET CH-9 Symmetry CLASS 6

ASSERTION-REASONING WORKSHEET

Chapter: Symmetry FOR DOWNLOAD PDF CLICK HERE
Class: 6 | NCERT Maths Chapter 9

✍🏽 Choose the correct option:
(A) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
(B) Both Assertion and Reason are true, but Reason is not the correct explanation.
(C) Assertion is true, but Reason is false.
(D) Assertion is false, but Reason is true.

Q1.

Assertion (A): A figure is symmetrical if it can be folded into two equal halves.
Reason (R): The line along which the figure is folded is called the line of symmetry.
Option: ___

Q2.

Assertion (A): A rectangle has two lines of symmetry.
Reason (R): Both horizontal and vertical lines divide it into equal halves.
Option: ___

Q3.

Assertion (A): A square has four lines of symmetry.
Reason (R): A square has all sides and angles equal.
Option: ___

Q4.

Assertion (A): A circle has exactly one line of symmetry.
Reason (R): A line of symmetry in a figure always passes through its center.
Option: ___

Q5.

Assertion (A): An equilateral triangle has three lines of symmetry.
Reason (R): All sides and angles of an equilateral triangle are equal.
Option: ___

Q6.

Assertion (A): The English letter “M” has a vertical line of symmetry.
Reason (R): Symmetry in alphabets depends on their geometric shapes.
Option: ___

Q7.

Assertion (A): All regular polygons have as many lines of symmetry as the number of sides.
Reason (R): Regular polygons have equal sides and angles.
Option: ___

Q8.

Assertion (A): A scalene triangle has three lines of symmetry.
Reason (R): Triangles always have at least one line of symmetry.
Option: ___

Q9.

Assertion (A): The letter “A” has a horizontal line of symmetry.
Reason (R): The upper and lower halves of “A” are mirror images.
Option: ___

Q10.

Assertion (A): A figure can have more than one line of symmetry.
Reason (R): Symmetrical figures may fold evenly along multiple lines.
Option: ___

Q11.

Assertion (A): Symmetry helps in understanding geometry and design.
Reason (R): Many patterns and designs are based on symmetrical shapes.
Option: ___

Q12.

Assertion (A): A parallelogram has no lines of symmetry.
Reason (R): Opposite sides of a parallelogram are equal but angles are not right angles.
Option: ___

Q13.

Assertion (A): Mirror symmetry is observed when an image appears exactly the same on the opposite side of a line.
Reason (R): A mirror acts like a line of symmetry.
Option: ___

Q14.

Assertion (A): A regular hexagon has 6 lines of symmetry.
Reason (R): It has 6 equal sides and 6 equal angles.
Option: ___

Q15.

Assertion (A): The letter “H” has both vertical and horizontal lines of symmetry.
Reason (R): Symmetrical letters can be used to explain line symmetry.
Option: ___

Q16.

Assertion (A): A line of symmetry always lies within the figure.
Reason (R): It must divide the figure into two equal parts.
Option: ___

Q17.

Assertion (A): An isosceles triangle always has two lines of symmetry.
Reason (R): It has two sides of equal length.
Option: ___

Q18.

Assertion (A): A rhombus always has two lines of symmetry.
Reason (R): Both diagonals of a rhombus are lines of symmetry.
Option: ___

Q19.

Assertion (A): A semicircle has one line of symmetry.
Reason (R): The straight edge of the semicircle can be folded over the curved edge.
Option: ___

Q20.

Assertion (A): Objects with symmetry are always more stable.
Reason (R): Symmetry helps in making designs that are balanced and aesthetic.
Option: ___
ANSWER KEY CLICK HERE

ASSERTION-REASONING WORKSHEET CH-8 Playing with Constructions CLASS 6

ASSERTION-REASONING WORKSHEET

Chapter: Playing with Constructions FOR DOWNLOAD PDF CLICK HERE
Class: 6 | NCERT Maths Chapter 8

✍🏽 Choose the correct option:
(A) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
(B) Both Assertion and Reason are true, but Reason is not the correct explanation.
(C) Assertion is true, but Reason is false.
(D) Assertion is false, but Reason is true.

Q1.

Assertion (A): A line segment of any length can be drawn using a ruler.
Reason (R): A ruler is a straightedge with marked lengths.
Option: ___

Q2.

Assertion (A): A circle can be drawn using a ruler and compass.
Reason (R): The compass is used to fix a radius and draw the curve.
Option: ___

Q3.

Assertion (A): A perpendicular bisector divides a line segment into two equal parts.
Reason (R): The perpendicular bisector intersects the line segment at a right angle.
Option: ___

Q4.

Assertion (A): A line can be constructed perpendicular to a given line using only a compass.
Reason (R): A compass allows equal arc constructions needed for perpendiculars.
Option: ___

Q5.

Assertion (A): The compass can be used to copy a line segment without using a ruler.
Reason (R): The compass can preserve the exact length when transferring.
Option: ___

Q6.

Assertion (A): Using only a ruler, one can construct a perfect 90° angle.
Reason (R): Angles need protractors or compass constructions for accuracy.
Option: ___

Q7.

Assertion (A): The intersection point of two arcs from ends of a line segment helps draw a perpendicular bisector.
Reason (R): The arcs from both ends intersect at equal distances from the segment’s midpoint.
Option: ___

Q8.

Assertion (A): A 60° angle can be constructed using a compass only.
Reason (R): An equilateral triangle’s angles are all 60°.
Option: ___

Q9.

Assertion (A): An angle of 30° can be constructed directly using only compass.
Reason (R): 30° is a basic geometric angle constructible by default.
Option: ___

Q10.

Assertion (A): A triangle can be constructed when three sides (SSS) are known.
Reason (R): The SSS criterion is sufficient for unique triangle construction.
Option: ___

Q11.

Assertion (A): Using compass and ruler, we can bisect any angle.
Reason (R): The method uses equal arcs and intersection points for accuracy.
Option: ___

Q12.

Assertion (A): An angle greater than 90° is called an obtuse angle.
Reason (R): Acute angles are greater than 90°.
Option: ___

Q13.

Assertion (A): The length of a line segment can be verified using a compass.
Reason (R): A compass can hold the fixed distance of a segment to compare.
Option: ___

Q14.

Assertion (A): All angles of a triangle can be constructed using compass and ruler.
Reason (R): Triangle construction methods include SSS, SAS, ASA.
Option: ___

Q15.

Assertion (A): A triangle can always be constructed from any three lengths.
Reason (R): The sum of two sides must always be greater than the third.
Option: ___

Q16.

Assertion (A): The compass is used to measure curved lengths.
Reason (R): Compass is a tool for drawing and measuring arcs and circles.
Option: ___

Q17.

Assertion (A): The midpoint of a line segment is the point that divides it equally.
Reason (R): The perpendicular bisector passes through the midpoint.
Option: ___

Q18.

Assertion (A): 90° angle can be constructed by bisecting a 60° angle.
Reason (R): 60° ÷ 2 = 90°
Option: ___

Q19.

Assertion (A): A protractor is used in constructions to measure and draw angles accurately.
Reason (R): It has degree markings from 0° to 180°.
Option: ___

Q20.

Assertion (A): Using compass and straightedge only, any angle can be constructed.
Reason (R): Only angles like 30°, 60°, 90°, 120° are constructible using classical methods.
Option: ___
ANSWER KEY CLICK HERE