Module 15: Lesson 7 Conditions for Rectangles, Rhombi, and Squares Characteristics of a Rectangle If a rectangle, then all 4 interior angles are right angles (Definition of a Rectangle) If a rectangle, then diagonals are congruent. If a rectangle, then both pairs of opposite sides are parallel. If a rectangle, then both pairs of opposite sides congruent. If a rectangle, then diagonals bisect each other. If a rectangle, then both pairs of opposite angles are congruent. If a rectangle, then consecutive angles are supplementary.

Characteristics of a Rhombus If a rhombus, then all 4 sides are congruent (Definition of a Rhombus). If a rhombus, then diagonals bisect both pairs of opposite angles. If a rhombus, then diagonals intersect perpendicularly. If a rhombus, then both pairs of opposite sides are parallel. If a rhombus, then both pairs of opposite sides congruent. If a rhombus, then diagonals bisect each other. If a rhombus, then both pairs of opposite angles are congruent. If a rhombus, then consecutive angles are supplementary.

Characteristics of a Square If a square, then all 4 sides are congruent. If a square, then diagonals bisect both pairs of opposite angles. If a square, then diagonals intersect perpendicularly. If a square, then all 4 interior angles are right angles. If a square, then diagonals are congruent. If a square, then both pairs of opposite sides are parallel. If a square, then both pairs of opposite sides congruent. If a square, then diagonals bisect each other. If a square, then both pairs of opposite angles are congruent. If a square, then consecutive angles are supplementary.

Conditions for a Rectangle Conditions for a Rhombus If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. Conditions for a Rhombus If one pair of consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus. 2) If the diagonals of a parallelogram intersect perpendicularly, then the parallelogram is a rhombus. 3) If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus. Conditions for a Square If both a rectangle and a rhombus, then the parallelogram is a square.

X Parallelogram Rectangle Rhombus Square Both Pairs of Opposite sides are parallel X Both Pairs of Opposite sides are congruent Diagonals Bisect each other Both Pairs of Opposite angles are congruent Consecutive angles are supplementary All 4 angles are right angles Both diagonals are congruent All 4 sides are congruent Diagonals intersect perpendicularly Both pairs of diagonals bisect opposite angles

Definitions Parallelogram – Quadrilateral with both pairs of opposite sides parallel. Rectangle – Quadrilateral with all 4 interior angles right angles. Rhombus – Quadrilateral with all 4 sides the same length. Square – Quadrilateral with all 4 sides the same length AND all 4 interior angles right angles.

Homework pages 808-810 #’s 1, 3-18 (all)