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Special Parallelograms

Special Parallelograms. SWBAT…. To use properties of diagonals of rhombi and rectangles To determine whether a parallelogram is a rhombus or a rectangle. Rectangles…. A rectangle is a quadrilateral with four right angles

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Special Parallelograms

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  1. Special Parallelograms

  2. SWBAT… • To use properties of diagonals of rhombi and rectangles • To determine whether a parallelogram is a rhombus or a rectangle.

  3. Rectangles… • A rectangle is a quadrilateral with four right angles • If both pairs of opposite angles are congruent, then it is a parallelogram

  4. Theorem • If a parallelogram is a rectangle, then its diagonals are congruent.

  5. Example 1 • Quadrilateral RSTU is a rectangle. If RT = 6x + 4 and SU = 7x – 4, find x. S R T U

  6. Example 2 • Find x and y if MNPL is a rectangle. 6y + 2 5x + 8 3x + 2

  7. Theorem • If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

  8. Example 3 • Determine whether parallelogram ABCD is a rectangle, given A (-2, 1), B (4, 3), C (5, 0) and D (-1, -2).

  9. Properties of Rhombi • A rhombus is a quadrilateral with all 4 sides are congruent. • The diagonals of a rhombus are perpendicular and congruent.

  10. Theorems • If the diagonals of a parallelogram are perpendicular then the parallelogram is a rhombus. • Each diagonal of a rhombus bisects a pair of opposite angles.

  11. Example 4 • Find y if angle 1 = y2 – 10. • Find <PNL if <MPL = 64 M L 1 Q N P

  12. Example 5 • Determine whether parallelogram ABCD is a rhombus, rectangle or a square for A(-4, -2), B(-2, 6), C(6, 4), D(4, -4). List all the apply.

  13. Find the values of V, W, X, Y and Z. SURE is a rectangle. • SR = 4v +2 EU = 6v – 8 • EC = 2w + 3 CU = 3w – 1 • m<1 = x m<2 = 2x • UR = 6y -7 SE = 4y – 1 • m<1 = 2z m<3 = 8z S U 2 c 3 1 R E

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