NSB31 Recap

Properties of geometric figures

Triangles

Classify by sides — equilateral (all equal), isosceles (two equal), scalene (none equal) — and by angles: acute, right or obtuse. Matching dashes on sides and matching arcs on angles show which are equal.

The angle sum of a triangle is 180∘180^\circ. In an isosceles triangle the base angles (opposite the equal sides) are equal, so one known angle unlocks the rest.

Three lengths only form a triangle if every pair of sides adds to more than the third: 2, 3 and 7 fail because 2+3<72 + 3 < 7. Construction questions give three sides and expect compass arcs: draw the base with a ruler, arc each remaining length from the ends, and join where the arcs cross — leave the arcs showing.

Quadrilateral properties

The angle sum of any quadrilateral is 360∘360^\circ. Know each shape’s property list:

  • Parallelogram: opposite sides parallel and equal, opposite angles equal, diagonals bisect each other, co-interior angles add to 180∘180^\circ.
  • Rhombus: a parallelogram with all sides equal; diagonals bisect each other at right angles and bisect the angles.
  • Rectangle: a parallelogram with four right angles; diagonals are equal.
  • Square: all of the above at once.
  • Trapezium: exactly one pair of parallel sides.
  • Kite: two pairs of adjacent equal sides; diagonals cross at right angles.

“List four properties of a square” is a real exam question — recite them from the list above.

The most precise name

When a diagram’s markings fit several names, give the most specific one the markings actually prove. Every square is a rhombus and a parallelogram, but calling a marked square “a parallelogram” loses the mark. Work down the chain — parallelogram, then rhombus or rectangle, then square — and stop at the last name the given information supports.

Symmetry

An axis (line) of symmetry folds the shape onto itself. Counts worth memorising: square 4, rectangle 2, rhombus 2, isosceles triangle 1, equilateral triangle 3, parallelogram 0, and a regular polygon has as many axes as sides (a regular hexagon has 6).

Rotational symmetry counts how many times a shape maps onto itself in a full turn — a parallelogram has none of the line kind but rotational symmetry of order 2.