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8-4 Rectangles

8-4 Rectangles. Properties of Rectangles. Quadrilateral with 4 right angles Opposite sides are congruent Opposite angles are congruent Consecutive angles are supplementary Diagonals are congruent and bisect each other Parallelogram. Examples:.

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8-4 Rectangles

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  1. 8-4 Rectangles

  2. Properties of Rectangles • Quadrilateral with 4 right angles • Opposite sides are congruent • Opposite angles are congruent • Consecutive angles are supplementary • Diagonals are congruent and bisect each other • Parallelogram

  3. Examples: • RSTU is a rectangle. If RT = 6x+4 and SU = 7x-4, find x • LMNP is a rectangle, find x and y S T R U 6y+2 5x+8 3x+2

  4. Diagonals • If the diagonals of a parallelogram are congruent then the parallelogram is a rectangle. • Ex: A contractor has been hired to pour a concrete patio. How can he be sure that the frame in which to pour the concrete is rectangular?

  5. On the coordinate plane • Find the slope of all sides • If the 2 consecutive sides have slopes that are opposite reciprocals then the sides are perpendicular (form right angles) • Opposite reciprocals

  6. Example: Is ABCD a rectangle if A(-2, 1) B(4, 3) C(5, 0) and D(-1, -2)

  7. 8-5 Rhombi and Squares

  8. Properties of Rhombi • Quadrilateral with 4 congruent sides • Diagonals are perpendicular • Each diagonal bisects a pair of opposite angles • If the diagonals of a parallelogram are perpendicular then the parallelogram is a rhombus • Has all the properties of a parallelogram

  9. Examples: • LMNP is a rhombus, Find y and m<PNL M 1 L N Q P m<1 = y2 – 54 m<MLP = 64

  10. Properties of a Square • Has all the properties of a parallelogram • Has all the properties of a rhombus • Has all the properties of a rectangle

  11. Square Rect. with 4 Congruent sides Rhombus Parallelogram With 4 congruent sides Rectangle Parallelogram With 1 rt < Parallelogram Opposite sides parallel

  12. Example: • Determine whether ABCD is a rhombus, a rectangle or a square for A(-2, -1) B(-1, 3) C(3, 2) and D(2, -2)

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