Quadrilateral and Triangle Construction

Essential Quadrilateral Properties

A quadrilateral is a polygon with four sides.
The interior angles of all quadrilaterals add up to 360 degrees.
A rectangle is a quadrilateral with four right angles.
A square is a quadrilateral with four equal sides and four right angles.
A parallelogram is a quadrilateral in which both pairs of opposite sides are equal and parallel. Its opposite angles are also equal.
A rhombus is a quadrilateral with all four sides equal in length. Opposite angles in a rhombus are equal.
A trapezium (known as a trapezoid in some texts) is a quadrilateral with one pair of parallel sides.
An isosceles trapezium (isosceles trapezoid) is a trapezium with equal length non-parallel sides and base angles.

Constructing Quadrilaterals

To construct a quadrilateral, one needs a minimum of five properties such as sides, angles or both.
A parallelogram can be constructed if the lengths of both pairs of opposite sides and one angle are known.
A rectangle can be constructed if the lengths of adjacent sides are known.
For a square, knowing the length of one side is sufficient.
A trapezium can be constructed if the lengths of the parallel sides, the distance between them, and one angle are known.

Mandatory Triangle Properties

A triangle is a polygon with three sides.
The sum of the interior angles of a triangle is always 180 degrees.
An equilateral triangle has all three sides of equal length and all three angles of 60 degrees.
An isosceles triangle has two sides of equal length, and the angles opposite these sides are equal.
A scalene triangle has sides of different lengths and angles of different measures.
A right-angled triangle has one angle of 90 degrees.

Constructing Triangles

To construct a triangle, one needs at least three properties such as sides, angles or both.
An equilateral triangle can be constructed knowing the length of one side.
An isosceles triangle can be constructed if the lengths of the equal sides and the angle between them are known.
A scalene triangle can be constructed if all three side lengths are known.
A right-angled triangle can be constructed if the lengths of two sides are known, one of which must be the hypotenuse.

Remember to always use a ruler or a straight edge and a pair of compasses where necessary for accurate constructions. Regular practice is essential in mastering these constructions.