Theorems involving Rectangles, Rhombuses & Squares

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High School Math based on the topics required for the Regents Exam conducted by NYSED.

The following diagram shows some theorems for rectangles, rhombuses, and squares. Scroll down the page for more examples and solutions on postulates and theorems for rectangles, rhombuses, and squares.

Rhombus Rectangle Square theorems & corollaries
Rhombus Corollary and Theorems
A quadrilateral is a rhombus if and only if it has four congruent sides.
Theorem
A parallelogram is a rhombus if and only if its diagonals are perpendicular.
Theorem
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.

Rectangle Corollary and Theorem
A quadrilateral is a rectangle if and only if it has four right angles.
Theorem
A parallelogram is a rectangle if and only if its diagonals are congruent.

Square Corollary
A quadrilateral is a square if and only if it is a rhombus and a rectangle.

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Conditions for Rectangles, Rhombuses, and Squares

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