Hard Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Name the polygon with the greatest number of sides among triangle, pentagon, and octagon.
Correct! Octagon has 8 sides, which is more than triangle (3) and pentagon (5).
(2) Write the number of diagonals in a pentagon.
Perfect! A pentagon has 5 diagonals. Formula:
(3) Name the type of triangle whose all sides are equal.
Excellent! An equilateral triangle has all three sides equal.
(4) Write the number of chords a circle can have.
Great! A circle can have infinitely many chords.
(5) Name the shape that has no sides and no vertices.
Correct! A circle is a curved shape with no sides or vertices.
Short Answer Questions (2 Marks Each)
Note: Answer each question with complete drawings, working, and clear explanations.
(1) Draw a triangle in which all sides are of different lengths and name it.
(2) Draw a regular hexagon and write the measure of each interior angle. Each interior angle of regular hexagon =
Perfect! Each interior angle of a regular hexagon is 120°.
(3) Draw a circle and show two radii and two diameters.
(4) Write two differences between a chord and a diameter.
(5) Draw a quadrilateral and mark all its diagonals.
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete drawings, working, and clear explanations.
(1) Draw a scalene triangle and mark its altitudes. Name the point where they meet.
(2) Draw a circle with center O, mark a chord AB, and draw the perpendicular bisector of AB.
(3) Draw two intersecting lines and name the angles formed. Write which angles are vertically opposite.
(4) Draw a rectangle and a square of the same side length. Compare their perimeters and areas.
(5) Draw a regular pentagon and a regular hexagon of the same side length. Compare the sum of their interior angles.
Pentagon:
Perfect! Hexagon has larger sum of interior angles than pentagon.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The number of diagonals in a hexagon is:
(a) 6 (b) 9 (c) 12 (d) 15
Correct! Using formula
(2) Which of the following is a regular polygon?
(a) Rectangle (b) Square (c) Trapezium (d) Kite
Correct! A square has all sides equal and all angles equal (90°).
(3) In a circle, a line segment joining any two points on the circle is called:
(a) Radius (b) Chord (c) Diameter (d) Tangent
Correct! A chord connects any two points on the circle.
(4) Which polygon has all its sides and angles equal?
(a) Regular polygon (b) Irregular polygon (c) Scalene triangle (d) Parallelogram
Correct! Regular polygons have all sides and angles equal.
(5) The sum of the interior angles of a pentagon is:
(a) 360° (b) 540° (c) 720° (d) 900°
Correct! Using formula (n-2)×180° = (5-2)×180° = 540°.
(6) Which of the following has only one curved surface?
(a) Sphere (b) Cube (c) Cone (d) Cylinder
Correct! A sphere has only one continuous curved surface.
(7) A polygon with 12 sides is called:
(a) Hexagon (b) Octagon (c) Decagon (d) Dodecagon
Correct! Dodecagon has 12 sides (dodeca = twelve).
(8) The number of lines of symmetry in a regular hexagon is:
(a) 2 (b) 3 (c) 4 (d) 6
Correct! A regular hexagon has 6 lines of symmetry.
(9) Which of the following is not a 2D shape?
(a) Triangle (b) Rectangle (c) Circle (d) Cube
Correct! A cube is a 3D shape with length, breadth, and height.
(10) The sum of the interior angles of a triangle is:
(a) 90° (b) 180° (c) 270° (d) 360°
Correct! The sum of interior angles of any triangle is always 180°.
Complex Geometry Challenge
Determine whether these statements are True or False:
Basic Geometric Ideas - Hard Quiz
🎉 Outstanding Achievement! Advanced Geometric Mastery:
You have successfully conquered the "Basic Geometric Ideas (Hard)" worksheet and mastered:
(1) Advanced Polygon Properties: Understanding diagonals, interior angles, and symmetry in complex polygons
(2) Triangle Classification: Distinguishing between equilateral, isosceles, and scalene triangles with their properties
(3) Regular Polygon Analysis: Identifying and analyzing regular polygons with equal sides and angles
(4) Circle Geometry: Understanding advanced circle concepts including chords, perpendicular bisectors, and infinite possibilities
(5) Angle Calculations: Computing interior angles using formulas for different polygons
(6) Diagonal Formulas: Applying the formula n(n-3)/2 to find number of diagonals in any polygon
(7) Geometric Constructions: Drawing complex figures with altitudes, perpendicular bisectors, and intersecting lines
(8) Symmetry Recognition: Identifying lines of symmetry in regular polygons and their properties
(9) 2D vs 3D Classification: Distinguishing between two-dimensional and three-dimensional shapes
(10) Vertically Opposite Angles: Understanding angle relationships in intersecting lines
(11) Comparative Analysis: Comparing perimeters, areas, and properties of different shapes
(12) Advanced Terminology: Using sophisticated geometric vocabulary including orthocenter, perpendicular bisector, etc.
(13) Formula Applications: Applying mathematical formulas for angles, diagonals, and geometric calculations
(14) Geometric Relationships: Understanding connections between different geometric concepts and properties
(15) Problem-Solving Integration: Combining multiple geometric concepts to solve complex problems
(16) Spatial Reasoning: Developing advanced visualization skills for complex geometric figures
Exceptional mastery! You've achieved advanced geometric understanding with mathematical sophistication!