6-4: Squares and Rhombi Expectations: G1.4.1: Solve multistep problems and construct proofs involving angle measure, side length, diagonal length, perimeter, and area of squares, rectangles, parallelograms, kites, and trapezoids. G1.4.2: Solve multistep problems and construct proofs involving quadrilaterals (e.g., prove that the diagonals of a rhombus are perpendicular) using Euclidean methods or coordinate geometry. 11/19/ : Squares and Rhombii

Rhombus Defn: Rhombus: A quadrilateral is a rhombus iff all 4 sides are congruent. The plural or rhombus is rhombi. 11/19/ : Squares and Rhombii

Properties of a Rhombus Theorem If a quadrilateral is a rhombus, then: a.it is a parallelogram. b. the diagonals are perpendicular to each other. c. each diagonal bisects a pair of opposite angles. 11/19/ : Squares and Rhombii

Prove a rhombus is a parallelogram. 11/19/ : Squares and Rhombii

The figure below is a rhombus. Solve for x. 10x x+12 11/19/ : Squares and Rhombii

Sufficient Condition for a Rhombus Theorem If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. 11/19/ : Squares and Rhombii

Determine the value of x so that the parallelogram is a rhombus. (15x – 30) 11/19/ : Squares and Rhombii

Square Defn: Square: A parallelogram is a square iff it is a rectangle and a rhombus. 11/19/ : Squares and Rhombii

What is true about the diagonals of a square? a.congruent (rectangle), b. perpendicular (rhombus), c. bisect a pair of opposite angles (rhombus), d. bisect each other (parallelogram) 11/19/ : Squares and Rhombii

WXYZ is a quadrilateral. Of the terms parallelogram, rectangle, rhombus, square which apply to WXYZ? W(5,5), X(10,5), Y(10,10), Z(5,10) 11/19/ : Squares and Rhombii

Which of the following is a property of squares, but not rhombi? A)Diagonals are perpendicular B)Diagonals are congruent C)Consecutive sides are congruent D)Consecutive angles are supplementary E)Opposite angles are congruent 11/19/ : Squares and Rhombii

Prove the diagonals of a square are congruent. 11/19/ : Squares and Rhombii

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Assignment Pages 317 – 318, # 21 – 35, 39 – 47 (odds) 11/19/ : Squares and Rhombii