Rectangles and Their Properties

The characterizations of a rectangle as described in the text are: a parallelogram with at least one right angle, a parallelogram with diagonals of equal length, a parallelogram where triangles ABD and DCA are congruent, an equiangular quadrilateral, a quadrilateral with four right angles, a quadrilateral where the two diagonals are equal in length and bisect each other, a convex quadrilateral with successive sides a, b, c, d whose area is $\frac{1}{4}(a+c)(b+d)$, and a convex quadrilateral with successive sides a, b, c, d whose area is $\frac{1}{2}\sqrt{(a^{2}+c^{2})(b^{2}+d^{2})}$.

The traditional hierarchy classification of a rectangle is not provided in the given text.

The two area formulas for a convex quadrilateral with successive sides a, b, c, d mentioned in the text are: $\frac{1}{4}(a+c)(b+d)$ and $\frac{1}{2}\sqrt{(a^{2}+c^{2})(b^{2}+d^{2})$.

<p>The conditions for a parallelogram to be classified as a rectangle are having at least one right angle and having diagonals of equal length.</p> Signup and view all the answers

<p>A rectangle is characterized based on its diagonals by having equal length diagonals.</p> Signup and view all the answers