“Basic Geometrical Ideas” Worksheet – Class 6 Math, Chapter 3 IMPORTANT » CBSE CYCLE

“Basic Geometrical Ideas” Worksheet – Class 6 Math, Chapter 3 IMPORTANT

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Chapter 2: Basic Geometrical Ideas

Total Marks: 60

Section A: Multiple Choice Questions (MCQs) – 20 Marks

Choose the correct answer from the options provided.

  1. What is the sum of angles in a triangle? a) 90 degrees b) 180 degrees c) 270 degrees d) 360 degrees
  2. A line that extends infinitely in both directions is called: a) Ray b) Line segment c) Line d) Plane.
  3. Which type of angle measures exactly 90 degrees? a) Acute angle b) Obtuse angle c) Right angle d) Straight angle
  4. How many diagonals does a rectangle have? a) 2 b) 3 c) 4 d) 5
  5. In a parallelogram, opposite sides are: a) Congruent b) Perpendicular c) Equal in length d) Parallel
  6. In a right triangle, what is the relationship between the lengths of the two shorter sides and the length of the hypotenuse? a) They are all equal b) The sum of the squares of the shorter sides equals the square of the hypotenuse c) The product of the shorter sides equals the hypotenuse d) The difference of the squares of the shorter sides equals the square of the hypotenuse
  7. What is the name of the point where two rays or line segments meet? a) Vertex b) Endpoint c) Intersection d) Midpoint
  8. If two angles add up to 180 degrees, they are called: a) Complementary angles b) Adjacent angles c) Supplementary angles d) Vertical angles
  9. What is the sum of the angles in a quadrilateral? a) 180 degrees b) 270 degrees c) 360 degrees d) 450 degrees
  10. Which of the following is not a type of triangle based on its angles? a) Equilateral triangle b) Isosceles triangle c) Acute triangle d) Scalene triangle
  11. What is the term for a closed figure with three or more sides, where each side is a line segment? a) Triangle b) Quadrilateral c) Polygon d) Circle
  12. What is the sum of the interior angles of a hexagon? a) 360 degrees b) 540 degrees c) 720 degrees d) 900 degrees
  13. Which type of angle is larger than 90 degrees but smaller than 180 degrees? a) Acute angle b) Obtuse angle c) Right angle d) Straight angle
  14. In a parallelogram, opposite angles are: a) Congruent b) Supplementary c) Equal in measure d) Perpendicular
  15. What is the term for a polygon with all sides and angles equal? a) Equilateral polygon b) Regular polygon c) Isosceles polygon d) Symmetrical polygon
  16. What do you call a quadrilateral with all sides of equal length and all angles right angles? a) Square b) Rectangle c) Rhombus d) Trapezoid
  17. In a triangle, the side opposite to the right angle is called the: a) Hypotenuse b) Base c) Adjacent side d) Opposite side
  18. What is the term for a line segment that connects two non-adjacent vertices in a polygon? a) Diagonal b) Radius c) Chord d) Diameter
  19. A triangle with all angles less than 90 degrees is known as a/an: a) Acute triangle b) Obtuse triangle c) Right triangle d) Equilateral triangle
  20. If two lines are perpendicular, what is the measure of the angles formed at their intersection? a) 45 degrees b) 90 degrees c) 180 degrees d) 360 degrees

Section B: Short Answer Questions – 10 Marks

  1. Define a point in geometry.
  2. Explain the difference between acute and obtuse angles.
  3. How is the area of a circle calculated?
  4. What is the Pythagorean theorem?
  5. State the property of vertically opposite angles.

Section C: Long Answer Questions – 5 Marks Each

  1. Describe the steps to construct a perpendicular bisector of a line segment.
  2. Explain the concept of supplementary angles with an example.
  3. Calculate the area of a triangle with a base of 8 cm and a height of 12 cm.
  4. Prove that the opposite sides of a parallelogram are congruent.
  5. Discuss the properties of an isosceles triangle.

Section D: Case-Based Study – 10 Marks

  1. A garden is in the shape of a rectangle with a length of 20 meters and a width of 15 meters. Calculate its perimeter and area. Also, explain how you arrived at your answers.

Section E: Concept Analytical Based – 5 Marks Each

  1. Compare and contrast acute, obtuse, and right angles.
  2. Discuss the significance of diagonals in a quadrilateral.

SOLUTION

Section A: Multiple Choice Questions (MCQs)

  1. Correct Answer: b) 180 degrees The sum of angles in a triangle is always 180 degrees.
  2. Correct Answer: c) Line A line extends infinitely in both directions.
  3. Correct Answer: c) Right angle A right angle measures exactly 90 degrees.
  4. Correct Answer: c) 4 A rectangle has four diagonals.
  5. Correct Answer: a) Congruent In a parallelogram, opposite sides are congruent.
  6. Correct Answer: b) The sum of the squares of the shorter sides equals the square of the hypotenuse This statement represents the Pythagorean theorem, a fundamental relationship in right triangles.
  7. Correct Answer: a) Vertex The point where two rays or line segments meet is called the vertex.
  8. Correct Answer: c) Supplementary angles When two angles add up to 180 degrees, they are called supplementary angles.
  9. Correct Answer: c) 360 degrees The sum of the angles in a quadrilateral is always 360 degrees.
  10. Correct Answer: a) Equilateral triangle An equilateral triangle has all sides and angles equal.
  11. Correct Answer: c) Polygon A polygon is a closed figure with three or more sides, where each side is a line segment.
  12. Correct Answer: a) 360 degrees The sum of the interior angles of a hexagon is 360 degrees.
  13. Correct Answer: b) Obtuse angle An obtuse angle measures more than 90 degrees but less than 180 degrees.
  14. Correct Answer: a) Congruent In a parallelogram, opposite angles are congruent.
  15. Correct Answer: b) Regular polygon A polygon with all sides and angles equal is called a regular polygon.
  16. Correct Answer: a) Square A quadrilateral with all sides of equal length and all angles right angles is a square.
  17. Correct Answer: a) Hypotenuse The side opposite the right angle in a triangle is called the hypotenuse.
  18. Correct Answer: a) Diagonal A line segment that connects two non-adjacent vertices in a polygon is called a diagonal.
  19. Correct Answer: a) Acute triangle A triangle with all angles less than 90 degrees is called an acute triangle.
  20. Correct Answer: b) 90 degrees If two lines are perpendicular, the angles formed at their intersection measure 90 degrees.

Section B: Short Answer Questions

  1. A point in geometry is a location in space with no dimensions.
  2. Acute angles measure less than 90 degrees, while obtuse angles measure more than 90 degrees.
  3. The area of a circle is calculated using the formula: Area = π × radius^2.
  4. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
  5. Vertically opposite angles are equal to each other.

Section C: Long Answer Questions

  1. To construct a perpendicular bisector of a line segment:
  • Place the compass on one endpoint of the segment and draw arcs on either side of the segment.
  • Repeat the above step using the other endpoint.
  • The intersection of the arcs is the midpoint of the segment.
  • Draw a line passing through the midpoint and perpendicular to the original segment.
  1. Supplementary angles add up to 180 degrees. For example, if one angle measures 120 degrees, the other angle must measure 60 degrees for their sum to be 180 degrees.
  2. Area of a triangle = (Base × Height) / 2 Area = (8 cm × 12 cm) / 2 = 48 cm²
  3. Opposite sides of a parallelogram are congruent. Let’s say the opposite sides are AB and CD. Then, AB = CD.
  4. In an isosceles triangle, two sides are equal in length. Additionally, the angles opposite the equal sides are also equal.

Section D: Case-Based Study

  1. Perimeter = 2 × (Length + Width) = 2 × (20 m + 15 m) = 70 meters Area = Length × Width = 20 m × 15 m = 300 square meters Explanation: The perimeter is calculated by adding all sides, and the area is calculated by multiplying length and width.

Section E: Concept Analytical Based

  1. Acute angles are less than 90 degrees, obtuse angles are greater than 90 degrees, and right angles are exactly 90 degrees. They all play different roles in geometry, affecting the relationships between lines and shapes.
  2. Diagonals of polygons help in understanding the internal angles and properties of the shape. In quadrilaterals, diagonals divide the shape into triangles and allow us to calculate various angles and side lengths.

Conclusion

Geometry is an exciting branch of mathematics that helps us understand the world around us in terms of shapes and spatial relationships. This worksheet has covered various aspects of basic geometrical ideas, from points and lines to angles, triangles, and quadrilaterals. Practice and understanding these concepts will lay a strong foundation for more advanced geometric explorations.

Frequently Asked Questions (FAQs)

  1. Q: How can I determine if two lines are parallel? A: Two lines are parallel if they never intersect, even when extended infinitely.
  2. Q: What is the importance of studying angles in geometry? A: Angles play a crucial role in determining the relationships between lines and shapes, aiding in problem-solving.
  3. Q: Why are diagonals important in polygons? A: Diagonals help in understanding the properties of polygons and calculating their internal angles.
  4. Q: Can you provide real-life examples of parallel lines and transversals? A: Railroad tracks and the beams of a bridge are examples of parallel lines, and a road intersecting multiple streets forms a transversal.
  5. Q: How do we use geometry in everyday life? A: Geometry is used in architecture, design, engineering, navigation, and various fields where spatial relationships are essential.

 

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Class 6th CBSE Math Chapter 4 – “Basic Geometrical Ideas” Notes And Important Questions » CBSE CYCLE

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