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GEOMETRY

GEOMETRY. 6.5 Rhombi and Squares. A rhombus is a parallelogram with four congruent sides. Diagonals of a Rhombus. Theorem 6.15: A parallelogram is a rhombus if and only if its diagonals are perpendicular.

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GEOMETRY

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  1. GEOMETRY 6.5 Rhombi and Squares

  2. A rhombus is a parallelogram with four congruent sides

  3. Diagonals of a Rhombus • Theorem 6.15: A parallelogram is a rhombus if and only if its diagonals are perpendicular.

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

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

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

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

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

  9. Example 2 • ABCD is a square.

  10. Venn Diagram parallelograms rhombi rectangles squares

  11. Example 3 • Determine if parallelogram QRST is a rhombus, rectangle, or square. Q(-2,-1), R(-1,2), S(4,1), T(3,-2)

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

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