All triangles have 3 interior angles that add up to 180 degrees and the 4 interior angles of a quadrilateral add up to 360 degrees but if 2 of its vertices are joined by a diagonal this marks out 2 interior triangles each having 3 interior angles adding to 180 degrees.
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When you draw the diagonals of a quadrilateral (a four-sided shape), they create triangles within the quadrilateral. These triangles are formed by connecting non-adjacent vertices of the quadrilateral. By understanding that the diagonals split the quadrilateral into smaller triangles, students can see how geometric shapes can be broken down and analyzed.
From ancient times, properties of quadrilaterals have been used especially in art, design and architecture. Diagonal of a rectangle divides it into two congruent triangles and the idea of congruency especially in triangles had been used by Egyptians to build The Great Pyramids of Giza!!!!! The idea of congruency of triangles initially from diagonal of quadrilaterals also helped Leonardo Da Vinci to paint the world famous 'Monalisa'!!!!! So, what other wonders do you want from quadrilaterals????!!!????
A quadrilateral is a parallelogram if and only if its diagonals bisect each other (this should be in any geometry book)
Corresponding parts of congruent triangles are congruent.
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