Properties Of Triangles And Quadrilaterals |top|

Triangles and quadrilaterals are the simplest polygons, yet they encode deep geometric structure. Understanding their properties is essential for topology, computer graphics, engineering, and proof-based mathematics. This paper proceeds from first principles, assuming only Euclid’s postulates and basic algebra.

Two pairs of adjacent sides are equal. One pair of opposite angles is equal, and diagonals intersect at 90°. Part 3: Relationship Summary Table Parallelogram Opposite sides parallel All sides equal All angles 90° Diagonals are equal Diagonals perpendicular Why These Properties Matter properties of triangles and quadrilaterals

One angle is exactly 90°. The side opposite this angle is the hypotenuse (the longest side). Obtuse: One angle is greater than 90°. Key Triangle Theorems Triangles and quadrilaterals are the simplest polygons, yet

Proof (synthetic): Through a vertex, draw a line parallel to the opposite side. Alternate interior angles give the sum of the three angles as a straight angle. Two pairs of adjacent sides are equal