Basic Geometrical Ideas (NCERT Ch. 4)

• Identify point, line segment, line, ray.
• Distinguish open and closed curves; identify interior, exterior, boundary.
• Recognise polygons (triangle, quadrilateral) — sides, vertices, diagonals.
• Identify angles, triangles (3 sides, 3 angles, 3 vertices), quadrilaterals (4 sides, 4 angles, 4 vertices, diagonals), and circles (centre, radius, diameter, chord, arc).

1. Point — an exact location, no length/width, marked with a dot.
2. Line segment — shortest path joining two points, has a fixed length.
3. Line — a line segment extended infinitely in both directions.
4. Ray — a portion of a line starting at one point and extending infinitely in one direction.
5. Curve — any drawing done without lifting a pencil; simple curve does not cross itself.
6. Polygon — a simple closed figure made of line segments (sides). A triangle has 3 sides, a quadrilateral has 4.
7. Diagonal — a line segment joining two non-adjacent vertices of a polygon.

A quadrilateral ABCD has vertices A, B, C, D. How many diagonals does it have?

Diagonals join non-adjacent vertices: AC and BD.
A quadrilateral has exactly 2 diagonals.

• Confusing a line (infinite) with a line segment (fixed length).
• Forgetting a ray has only one endpoint.
• Counting adjacent vertices as forming a diagonal (they form a side, not a diagonal).

• Name the parts of a circle: centre, radius, diameter, chord, arc.
• Draw a simple closed curve that is not a polygon.

Open the Practice tab for graded questions on Basic Geometrical Ideas (NCERT Ch. 4).