Basic Geometrical Ideas

Geometry is built from a few basic ideas. A point marks an exact position and is named by a capital letter such as A. The shortest path joining two points A and B is the line segment AB, which has a definite length. Extending it endlessly in both directions gives a line, while a ray starts at a point and goes on endlessly in one direction. Two lines that meet at a point are intersecting lines, and lines in a plane that never meet are parallel lines, like the opposite edges of a ruler. The chapter then studies curves, which can be open or closed and simple or crossing themselves, and polygons, simple closed figures made only of line segments, with sides, vertices, adjacent sides and diagonals. You will learn about angles, with their vertex, arms, interior and exterior, and about triangles and quadrilaterals. Finally, it explores the circle and its parts: centre, radius, diameter, chord, arc, sector, segment and circumference.

Detailed Worksheet: Basic Geometrical Ideas Section A - Definitions (10 marks) 1. Define a line segment and a ray. State one difference between them and give one real-life example of each. (2 marks) 2. What are intersecting lines and parallel lines? Give one example of each from your classroom. (2 marks) 3. What is a polygon? Explain the terms adjacent sides and diagonal of a polygon. (2 marks) 4. Define an angle. Name the vertex and arms of angle PQR. (2 marks) 5. Define the radius, diameter and chord of a circle. Which chord is the longest? (2 marks) Section B - Calculations and Applications (15 marks) 6. Mark four points A, B, C and D in such a way that no three of them lie on the same line. (i) How many line segments can be drawn joining these points in pairs? (ii) Name all of them. (iii) How many line segments can be drawn using five such points? (3 marks) 7. The radius of a circular plate is 7 cm. (i) Find its diameter. (ii) Another circle has a diameter of 18 cm; find its radius. (iii) Can a chord of the first circle be 16 cm long? Give a reason. (3 marks) 8. In a quadrilateral PQRS, name (i) all four sides (ii) the pairs of opposite sides (iii) the pairs of adjacent sides (iv) the two diagonals (v) the pairs of opposite angles (vi) the four angles. (3 marks) 9. A clock shows 3 o'clock. (i) Name the angle formed by its hands using three letters if the centre is O, the tip of the hour hand is H and the tip of the minute hand is M. (ii) Is a point near the 1 on the dial in the interior or the exterior of angle HOM? (iii) Is a point near the 7 in the interior or the exterior? (3 marks) 10. Count and name: (i) the number of diagonals of a quadrilateral (ii) the number of diagonals of a pentagon (iii) the number of vertices and sides of a hexagon. Draw a rough figure to support each answer. (3 marks) Section C - Diagrams (10 marks) 11. Draw a circle with centre O. Draw and label a radius OA, a diameter BC, a chord PQ, an arc, a sector and a segment. Shade the minor segment and mark the circumference. (4 marks) 12. Draw a triangle ABC. Mark a point P in its interior, a point Q in its exterior and a point R on the triangle. Name the three sides and the three angles. (3 marks) 13. Draw rough figures of (i) an open curve (ii) a closed curve that is not simple (iii) a simple closed curve. In the simple closed curve, mark one point each in the interior, exterior and on the boundary. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Four lines are drawn on a sheet of paper. (i) What is the greatest number of points at which they can intersect? (ii) What is the least number of intersection points? (iii) Draw a figure for the greatest case. (iv) Explain why two distinct lines can meet at no more than one point. (5 marks) 15. A student says, "Every closed figure is a polygon." (i) Is this true? Give a counter-example. (ii) Which of these are polygons: a triangle, a circle, a square, a figure 8 drawn with a curved line? (iii) Explain why a figure with only three line segments that is closed is always a triangle. (iv) Why is a circle not a polygon? (5 marks) 16. Look at the letter shapes E, O, N, L and S. (i) Which are made only of line segments? (ii) Which is a simple closed curve? (iii) Which shapes contain parallel line segments? (iv) Which contain intersecting line segments? (v) Explain whether the letter O can have a diagonal. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Use a sharp pencil and ruler for all figures and label every point with a capital letter.