Level 1 — RecognitionBasic Geometry

Basic Geometry

30 marksprintable — key stays hidden on paper

Time: 20 minutes Total Marks: 30

Instructions: Answer all questions. For True/False items you must give a short justification. Use $\pi = 3.14$ where needed.

Section A — Multiple Choice (1 mark each)

Choose the single correct option.

Q1. Which has two endpoints and a fixed length? (a) line (b) ray (c) line segment (d) point

Q2. An angle measuring $125^\circ$ is: (a) acute (b) right (c) obtuse (d) reflex

Q3. The complement of a $40^\circ$ angle is: (a) $140^\circ$ (b) $50^\circ$ (c) $60^\circ$ (d) $320^\circ$

Q4. When a transversal crosses two parallel lines, alternate angles are: (a) supplementary (b) equal (c) complementary (d) reflex

Q5. A triangle with all sides of different length is called: (a) equilateral (b) isosceles (c) scalene (d) right

Q6. A quadrilateral with exactly one pair of parallel sides is a: (a) rhombus (b) trapezium (c) kite (d) rectangle

Q7. A chord that passes through the centre of a circle is the: (a) radius (b) arc (c) diameter (d) sector

Q8. The circumference of a circle of radius $r$ is: (a) $\pi r^2$ (b) $2\pi r$ (c) $\pi d^2$ (d) $\tfrac12 \pi r$

Q9. A 3D shape with 6 identical square faces is a: (a) cuboid (b) cylinder (c) cube (d) prism

Q10. The order of rotational symmetry of a square is: (a) 1 (b) 2 (c) 3 (d) 4

Section B — Matching (5 marks)

Q11. Match each shape/term to its property. Write pairs like A–iii.

Column X	Column Y
A. Rectangle	i. All sides equal, all angles $90^\circ$
B. Square	ii. Opposite sides equal, all angles $90^\circ$
C. Straight angle	iii. Boundary length of a polygon
D. Perimeter	iv. Measures exactly $180^\circ$
E. Radius	v. Half of the diameter

Section C — True / False with justification (2 marks each: 1 verdict + 1 reason)

Q12. The interior angles of any triangle add up to $180^\circ$ .

Q13. All rectangles are squares.

Q14. Two angles that are supplementary add up to $90^\circ$ .

Q15. A cube has 12 edges.

Q16. A parallelogram has exactly two lines of symmetry.

Q17. The exterior angle of a triangle equals the sum of the two opposite interior angles.

Q18. Perpendicular lines meet at a $90^\circ$ angle.

Q19. The area of a triangle with base $b$ and height $h$ is $b \times h$ .

Q20. A net of a cube is made of 6 squares.

Answer keyMark scheme & solutions

Section A (1 mark each)

Q1. (c) line segment — a segment is bounded by two endpoints; a line/ray are unbounded. (1)

Q2. (c) obtuse — $125^\circ$ lies between $90^\circ$ and $180^\circ$ . (1)

Q3. (b) $50^\circ$ — complementary angles sum to $90^\circ$ ; $90-40=50$ . (1)

Q4. (b) equal — alternate angles between parallel lines are congruent. (1)

Q5. (c) scalene — no two sides equal. (1)

Q6. (b) trapezium — defined by exactly one pair of parallel sides. (1)

Q7. (c) diameter — longest chord, through the centre. (1)

Q8. (b) $2\pi r$ — standard circumference formula ( $\pi r^2$ is area). (1)

Q9. (c) cube — six congruent square faces. (1)

Q10. (d) 4 — a square maps onto itself at $90^\circ,180^\circ,270^\circ,360^\circ$ . (1)

Section B

Q11. A–ii, B–i, C–iv, D–iii, E–v. (1 mark each correct pair = 5)

Section C (1 verdict + 1 reason)

Q12. True. Angle sum property of a triangle is exactly $180^\circ$ . (2)

Q13. False. A square requires all four sides equal; a rectangle only needs opposite sides equal, so not every rectangle is a square (though every square is a rectangle). (2)

Q14. False. Supplementary angles sum to $180^\circ$ ; those summing to $90^\circ$ are complementary. (2)

Q15. True. A cube has 6 faces, 8 vertices and 12 edges. (2)

Q16. False. A general parallelogram has no lines of symmetry (it has rotational symmetry of order 2). (2)

Q17. True. Exterior angle theorem: exterior angle = sum of two remote interior angles. (2)

Q18. True. By definition perpendicular lines intersect at $90^\circ$ . (2)

Q19. False. Correct formula is $\tfrac12 b h$ ; the given expression is twice the area. (2)

Q20. True. A cube has 6 square faces, so its net consists of 6 squares. (2)

[
{"claim":"Complement of 40 degrees is 50","code":"result = (90 - 40 == 50)"},
{"claim":"Triangle angle sum is 180","code":"result = (60 + 60 + 60 == 180)"},
{"claim":"Cube has 12 edges (Euler: V-E+F=2, V=8,F=6)","code":"V,F=8,6; E=V+F-2; result = (E==12)"},
{"claim":"Area of triangle is half base times height, not base times height","code":"b,h=symbols('b h'); result = (Rational(1,2)*b*h != b*h)"}
]