Mathematics (AKU-MTH)Angles on a straight line sum to 180° Angles at a point sum to 360° Vertically opposite angles are equal Interior angles of a triangle sum to 180°; quadrilateral to 360°
Alternate angles (Z-shape) — equal Co-interior angles (C-shape) — add to 180° Corresponding angles (F-shape) — equal
Rectangle: A = l × w Triangle: A = ½ × base × height Circle: A = πr², Circumference = 2πr Cylinder: V = πr²h, Total SA = 2πr² + 2πrh Cone: V = ⅓πr²h Sphere: V = ⁴⁄₃πr³
Topic 3 of 7Aga Khan Board
Geometry & Measurement
Properties of shapes, angles, area, volume and constructions
Angles:
Parallel lines cut by a transversal create:
Areas and Volumes:
Pythagoras' theorem: In a right-angled triangle, a² + b² = c² (c = hypotenuse).
Construction skills: bisecting angles, perpendicular bisectors, constructing triangles using ruler and compass.
Key Points to Remember
- 1Angles in triangle = 180°; quadrilateral = 360°
- 2Alternate and corresponding angles are equal
- 3Circle area = πr², cylinder volume = πr²h
- 4Pythagoras: a² + b² = c²
Pakistan Example
Rooftop Water Tanks in Karachi — Volume Calculations
A standard Karachi rooftop water tank is cylindrical with radius 0.6 m and height 1.5 m. Volume = π(0.6)²(1.5) ≈ 1.696 m³ ≈ 1696 litres. Families in areas with water shortages (like parts of Lyari or SITE) calculate this to plan daily usage. Geometry is a daily survival skill.