 Both pairs of opposite sides are parallel  Both pairs of opposite sides are congruent  The opposite angles are congruent  The diagonals bisect each other  Any pair of consecutive angles are supplementary

II suppl.

 Has all properties of a parallelogram  All angles are right angles  Diagonals are congruent

 Two disjoint pairs of consecutive sides are congruent  The diagonals are perpendicular  One diagonal is the perpendicular bisector of the other  One of the diagonals bisects a pair of opposite angles  One pair of opposite angles are congruent

 Has all properties of a parallelogram and of a kite (half properties become full properties  All sides are congruent  The diagonals bisect the angles  The diagonals are perpendicular bisectors of each other  The diagonals divide the rhombus into four congruent right triangles

 Has all properties of a rectangle and a rhombus  The diagonals form four isosceles right triangles

 The legs are congruent  The bases are parallel  The lower base angles are congruent  The upper base angles are congruent  The diagonals are congruent  Any lower base angle is supplementary to any upper base angle

Given: ABCD is a rectangle DA = 5x CB = 25 DC = 2x Find: a.) The value of x b.) The perimeter of ABCD a.) 5x = 25 x = 5 b.) DA= 25 CB = 25 DC = 10 AB = 10 Perimeter = Perimeter = 70

Given: ABCD is a parallelogram Prove: ABCD is a rectangle StatementsReasons 1. ABCD is a parallelogram 1. Given 2.2. Given 3. <DAB is a right < 3. Perpendicular lines form right <s 4. ABCD is a rectangle 4. If a parallelogram contains at least one right <, it is a rectangle

Given: ABCD is a parallelogram <DAB = n <ABC = 2n Find: m <BCD and m < ADC 2n+n=180 3n=180 n=60 2n=120 m <BCD = 60 m<ADC = 120

Given: ABCD is a rhombus AB = 2x-5 BC = x a.) Find the value of x b.) Find the perimeter

Given: ABCD is a parallelogram Prove: ▲AED ▲BEC

Given: m<CAB = n m<CDB = 4n AD = 2n-53 Find: a.) AD b.) m<ACD

2x-5 = x X = 5 AB = 2x-5 AB = 5 Perimeter = Perimeter = 20

StatementsReasons 1. ABCD is a parallelogram1. Given 2.2. In a parallelogram, opp. Sides are congruent 3. Bisects3. In a parallelogram, diagonals bisect each other 4.4. If a ray bisects a segment, it divides the segment into 2 congruent segments 5. Bisects5. Same as Same as 4 7. ▲AED ▲BEC7. SSS (2,4,6)

n + 4n = 180 5n = 180 n = 36 4n = 144 2n-53 = 19 Therefore, AD = 19 m<ACD = 144 (In an isosceles trapezoid, upper base angles are congruent)

Rhoad, Richard, George Milauskas, and Robert Whippie. Geometry for Enjoyment and Challenge. New Edition. Evanston, Illinois: McDougall, Littell & Company, Print.