6.5 Rhombi and Squares GEOMETRY. A rhombus is a parallelogram with four congruent sides.

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Presentation transcript:

6.5 Rhombi and Squares GEOMETRY

A rhombus is a parallelogram with four congruent sides

D IAGONALS OF A R HOMBUS  Theorem 6.15: A parallelogram is a rhombus if and only if its diagonals are perpendicular.

 Theorem 6.16: A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.

Theorem 6.19  If one pair of consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.

E XAMPLE 1 Find x, y, and z. (6x + 30)° ABCD is a rhombus. C B A D 18 2z-2 (7y -2)° (3y +10)°

 A square is a parallelogram with 4 congruent sides and 4 right angles.

Theorem 6.20  If a parallelogram is a rhombus and a rectangle, then it is a square.

E XAMPLE 2  ABCD is a square.

Venn Diagram parallelograms rhombirectangles squares

E XAMPLE 3  Determine if parallelogram QRST is a rhombus, rectangle, or square. Q(-2,-1), R(-1,2), S(4,1), T(3,-2)

H OMEWORK Worksheet and… Page 431: (7-12, 23-33, 55-60) all