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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 AB DC AD BC AB II DC AD II BC DAB BCD ADC ABC DAB suppl. ABC BCD suppl. ADC AE EC DE EB 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 = 25 + 25 + 10 + 10 Perimeter = 70 Given: ABCD is a parallelogram AD AB Prove: ABCD is a rectangle Statements Reasons 1. ABCD is a parallelogram 1. Given 2. AD AB 3. <DAB is a right < 2. Given 4. ABCD is a rectangle 4. If a parallelogram contains at least one right <, it is a rectangle 3. Perpendicular lines form right <s 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 = 5 + 5 + 5 + 5 Perimeter = 20 Statements Reasons 1. ABCD is a parallelogram 1. Given 2. BC AD 2. In a parallelogram, opp. Sides are congruent 3. AC Bisects BD 3. In a parallelogram, diagonals bisect each other 4. BE ED 4. If a ray bisects a segment, it divides the segment into 2 congruent segments 5. BD Bisects AC 5. Same as 3 6. AE EC 7. ▲AED ▲BEC 6. Same as 4 7. 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, 1997. 241-248. Print.