CHAPTER 5: QUADRILATERALS 5-4: Special Quadrilaterals

RECTANGLES A rectangle is a quadrilateral that has four right angles. Because both pairs of opposite angles of a rectangle are congruent, a rectangle is a parallelogram.

RHOMBUS A rhombus is a quadrilateral that has four congruent sides. Because both pairs of opposite sides of a rhombus are congruent, every rhombus is a parallelogram.

SQUARE A square is a quadrilateral with four right angles and four congruent sides. Because both pairs of opposite angles and sides are congruent, all squares are parallelograms.

THEOREM 5-12 THEOREM 5-12 The diagonals of a rectangle are congruent.

THEOREM 5-13 THEOREM 5-13 The diagonals of a rhombus are perpendicular.

THEOREM 5-14 THEOREM 5-14 Each diagonal of a rhombus bisects two angles of the rhombus.

THEOREM 5-15 THEOREM 5-15 The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.

THEOREM 5-16 THEOREM 5-16 If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle.

THEOREM 5-17 THEOREM 5-17 If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.

ALWAYS, SOMETIMES, NEVER A square is ______ a rhombus. The diagonals of a parallelogram ______ bisect the angles of the parallelogram. A quadrilateral with one pair of sides congruent and one pair parallel is ______ a parallelogram. The diagonals of a rhombus are ______ congruent.

ALWAYS, SOMETIMES, NEVER A rectangle ______ has consecutive sides congruent. A rectangle ______ has perpendicular diagonals. The diagonals of a rhombus ______ bisect each other. The diagonals of a parallelogram are ______ perpendicular bisectors of each other. Sometimes Always sometimes

Quadrilateral ABCD is a Rhombus. Find the measure of each angle. 62 D C ACD DEC EDC ABC 62 90 28 56

Quadrilateral MNOP is a rectangle. Complete: 29 12 L P O m PON = m PMO = PL = MO = 90 61 12 24

∆ABC is a right ∆; M is the midpoint of AB. If AM = 7, then MB = _____, AB = _____, and CM = _____. If AB = x, then AM = _____, MB = _____, and MC = _____. 7, 14, 7 x/2, x/2, x/2

CLASSWORK/HOMEWORK Pg. 186, Classroom Exercises 1-11 Pg. 187, Written Exercises 2-18 even.