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"Are you really sure that a floor can't also be a ceiling?" M.C. Escher Rectangles • • • • • A rectangle is a quadrilateral with four right angles. A rectangle is a parallelogram. A rectangle has opposite congruent sides. Diagonals of a rectangle bisect each other. The diagonals of a rectangle are congruent. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. 6.4 Rectangles Check.3.2 Connect coordinate geometry to geometric figures in the plane (e.g. midpoints, distance formula, slope, and polygons). Spi.3.2 Use coordinate geometry to prove characteristics of polygonal figures. Check.4.10 Identify and apply properties and relationships of special figures (e.g., isosceles and equilateral triangles, family of quadrilaterals, polygons, and solids). "Are you really sure that a floor can't also be a ceiling?" M.C. Escher Rectangles • • • • • A rectangle is a quadrilateral with four right angles. A rectangle is a parallelogram. A rectangle has opposite congruent sides. Diagonals of a rectangle bisect each other. The diagonals of a rectangle are congruent. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. Objective: To be able to identify rectangles and understand and apply properties. Diagonals of a Rectangle • Quadrilateral MNOP is a rectangle. • If MO=6x + 14 and PN = 9x+5, • Find x. 6x + 14 = 9x + 5 9 = 3x 3=x Angles of a Rectangle • Quadrilateral ABCD is a rectangle. • Find x and y 4y + 4 = y2 -1 4x + 5 + 9x + 20 = 90 13x +25 = 90 13x = 65 x=5 Disregard y=-1, negative angle 0= y2 -4y -5 0= (y-5)(y+1) y = 5 or y=-1 Coordinate Plane Determine if Quadrilateral FGHJ is a rectangle given vertices at F(-4, -1), G(-2, -5), H(4, -2), J(2,2) Perpendicular lines form Right Angles Slopes of perpendicular lines are opposite inverses Sides consecutive sides are perpendicular making this a rectangle. Also could have used distance formula Summary • Rectangle is a special parallelogram which is a special quadrilateral. • Rectangle has all the properties of a parallelogram • Plus in a rectangle all angles are right angles and the diagonals of a rectangle are congruent. • Practice Assignment – Page 422, 10 - 30 even