Hard Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) What is the radius of a circle whose diameter is 9 cm?
Correct! Radius = diameter ÷ 2 = 9 ÷ 2 = 4.5 cm.
(2) Which construction is required to locate the centre of a circle?
Perfect! The center is found by constructing perpendicular bisectors of any two chords.
(3) Define angle bisector. Line that
Excellent! An angle bisector divides an angle into two equal parts.
(4) What is the measure of each angle in an equilateral triangle?
Great! Each angle in an equilateral triangle measures 60°.
(5) How many right angles are there in a straight angle?
Correct! A straight angle (180°) contains two right angles (90° each).
Short Answer Questions (2 Marks Each)
Answer each question with detailed construction steps
(1) Draw a line segment of 8 cm and construct its perpendicular bisector.
(2) Construct an angle of 45° using a compass.
(3) Draw a circle of radius 6 cm and mark two diameters perpendicular to each other.
(4) From a point outside a line, draw a perpendicular to the line.
(5) Construct an angle of 135° using ruler and compass.
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete steps and clear explanations.
(1) Draw a line segment of 10 cm and divide it into four equal parts using compass and ruler.
(2) Construct angles of 15°, 30°, 45°, and 60° using only a compass and ruler.
(3) Draw a circle of radius 4 cm. Construct a tangent to it from a point on the circle.
(4) From a point outside a circle of radius 3 cm, draw a line touching the circle.
(5) Draw a perpendicular bisector of a line segment AB = 12 cm, and show that it passes through the midpoint of AB.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The radius of a circle of diameter 10 cm is:
(a) 2 cm (b) 5 cm (c) 8 cm (d) 10 cm
Correct! Radius = diameter ÷ 2 = 10 ÷ 2 = 5 cm.
(2) The angle bisector divides an angle into:
(a) Two equal parts (b) Three equal parts (c) Four equal parts (d) Unequal parts
Correct! An angle bisector divides an angle into two equal parts.
(3) The measure of each angle of an equilateral triangle is:
(a) 30° (b) 45° (c) 60° (d) 90°
Correct! Each angle in an equilateral triangle measures 60° (180° ÷ 3 = 60°).
(4) A perpendicular bisector always passes through the:
(a) Endpoint (b) Midpoint (c) Any point (d) Arc
Correct! A perpendicular bisector always passes through the midpoint of a line segment.
(5) The sum of angles on a straight line is:
(a) 90° (b) 120° (c) 150° (d) 180°
Correct! The sum of angles on a straight line is always 180°.
(6) Select all correct options: Which instrument is used to construct an angle of 135° exactly?
(a) Ruler only (b) Compass and ruler (c) Protractor (d) Divider
Correct! Both compass and ruler, or protractor can construct 135° exactly.
(7) The perpendicular to a line from a point outside it meets the line at:
(a) Any point (b) Midpoint (c) Foot of perpendicular (d) None
Correct! The point where the perpendicular meets the line is called the foot of perpendicular.
(8) If a circle has radius 7 cm, its diameter is:
(a) 7 cm (b) 10 cm (c) 14 cm (d) 21 cm
Correct! Diameter = 2 × radius = 2 × 7 = 14 cm.
(9) A tangent to a circle touches the circle at:
(a) Two points (b) Three points (c) One point only (d) No point
Correct! A tangent touches a circle at exactly one point.
(10) Select all correct options: The construction of 45° is done by:
(a) Halving 30° (b) Halving 60° (c) Halving 90° (d) Adding 30° and 15°
Correct! 45° is constructed by halving a 90° angle, or by adding 30° and 15°.
Expert Geometry Challenge
Determine whether these statements are True or False:
Expert Geometry Mastery Quiz
🎉 Congratulations! What You've Mastered:
You have successfully completed the "Expert Practical Geometry" worksheet and learned:
(1) Advanced Angle Constructions: Mastering complex angles (15°, 45°, 135°) using sophisticated compass techniques
(2) Line Division Mastery: Dividing line segments into multiple equal parts using systematic bisection methods
(3) Tangent Constructions: Drawing tangents to circles from both internal and external points
(4) Circle Center Location: Finding circle centers using perpendicular bisectors of chords
(5) External Perpendicular Constructions: Advanced techniques for perpendiculars from external points
(6) Multi-step Geometric Proofs: Verifying constructions through measurement and logical reasoning
(7) Precision in Complex Constructions: Maintaining accuracy in multi-step geometric procedures
(8) Advanced Circle Geometry: Understanding tangent properties and circle-line relationships
(9) Systematic Problem-solving: Breaking complex constructions into manageable steps
(10) Geometric Verification: Proving construction accuracy through measurement and geometric principles
Exceptional achievement! You have mastered expert-level practical geometry and can handle the most challenging constructions with precision and mathematical rigor!