Every quadrilateral can be split into two triangles by drawing a diagonal. The reverse is also true. If we take two triangles and join them along an equal side, the outer boundary forms a quadrilateral. The quadrilateral we get depends on the type of triangles we start with.
Joining triangles
Case 1: A quadrilateral formed from two equilateral triangles.
When \(2\) equilateral triangles are joined along one side:
- All four sides of the new figure become equal.
- Opposite sides become parallel.
Example:
Let us consider two equilateral triangles of length \(3 \ cm\), and join them along one side.
The quadrilateral formed is a rhombus because all four sides are equal and opposite sides are parallel.
Case 2: A quadrilateral formed from joining two isosceles triangles
(a) Joining along the unequal side
When two isosceles triangles are joined along the unequal side, then the resulting quadrilateral has:
- Two pairs of adjacent sides are equal.
- One pair of opposite angles are equal.
The quadrilateral formed is a kite.
(b) Joining along the equal side
When two isosceles triangles are joined along the equal side, then the resulting quadrilateral has:
- Opposite sides are equal and parallel
The quadrilateral formed is a parallelogram.
Depending on orientation, joining them along an equal side may produce:
- a kite,
- a rhombus,
- a parallelogram.
The result depends on how the triangles are reflected before joining.
Example:
Let us consider two isosceles triangles of length \(5 \ cm\), \(5 \ cm\) and \(7 \ cm\).
Case 3: A quadrilateral formed from joining two scalene triangles.
Example:
Let us consider two scalene triangles of length \(2 \ cm\), \(3 \ cm\) and \(4 \ cm\) and join along the sides.
