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A quadrilateral is a four sided figure but it does not have to be a rectangle, square or parallelogram. Instead it can be a v-shaped concave figure and still have four sides. Therefore, with this  quadrilateral a triangle can intersect with it 8 times.

→A Quadrilateral is four sided Polygon.

→And ,A Triangle is three sided polygon.

⇒Take any kind of Quadrilateral(Parallelogram,Square,Rectangle,Rhombus,Trapezoid,Kite), and any type of Triangle (Scalene, Isosceles,or Equilateral,Right,Obtuse,Acute),there can be Maximum of six Intersection point between a quadrilateral and a triangle.

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