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Quadrilaterals

Quadrilaterals. Sara Beberman Olivia DeFlumeri Olivia Huynh Amanda Okaka. A. KITE. PROPERTIES Two sets of adjacent sides are congruent One set of congruent angles opposite each other Diagonals are perpendicular The longer diagonal of the kite bisects the shorter diagonal. D. E.

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Quadrilaterals

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  1. Quadrilaterals Sara Beberman Olivia DeFlumeri Olivia Huynh Amanda Okaka

  2. A KITE • PROPERTIES • Two sets of adjacent sides are congruent • One set of congruent angles opposite each other • Diagonals are perpendicular • The longer diagonal of the kite bisects the shorter diagonal D E B -A quadrilateral with two distinct pairs of congruent adjacent sides. C • AB≅AD, DC≅BC, (Two sets of congruent adjacent sides) • AE is perpendicular to DB • DE≅EB (The longer diagonal bisects the shorter diagonal) • <ADC≅<ABC (One set of angles congruent)

  3. Rhombus Rhombus: a parallelogram with a pair of congruent adjacent sides Properties: • Opposite sides are congruent and parallel • AB  BC  CD  DA AB // CD and BC // DA • Opposite angles are congruent ABC ADC andBAD BCD • Consecutive angles are supplementary BAD + ABC = 180andADC + DCB = 180 BAD + ADC = 180andABC + DCB =180 • Diagonals bisect each other BO  DO and AO  CO • Diagonals are perpendicular AOB = BOC = COD = DOA = 90 • The diagonals bisect the angles BAC DAC, ABD CBD, BCA DCA, andCDB ADB

  4. Trapezoid Trapezoid: A quadrilateral, which has only one set of opposite sides parallel Properties: • Exactly one pair of opposite sides is parallel BC//AD • Consecutive angles on different bases are supplementary DAB + ABC = 180 and ADC + BCD = 180

  5. Rectangle • Properties of a Rectangle • both pairs of opposite sides are congruent and parallel • diagonals are congruent • diagonals bisect one another • consecutive angles are supplementary • both pairs of opposite angles are congruent • has 4 right angles Definition – A rectangle is a parallelogram that has four right angles, 2 sets of opposite sides congruent, and congruent diagonals • Ex. • * AB is Congruent and Parallel to DC, AD is Congruent and Parallel to BC • * Diagonal X and Diagonal Y are Congruent and bisect one another • * <A + <D = 180˚, <B + <C = 180˚, <A + <B = 180˚, <D + <C = 180˚ • <A ≅<C, <B≅<D • <A, <B, <C, and <D are all right angles (each equal 90˚) A B X Y C D

  6. Square * Definition – A parallelogram with all right angles and all side lengths congruent • Properties of a Square: • All sides are congruent • Opposite sides are parallel • All angles are congruent (all right angles) • Consecutive angles are supplementary • Diagonals are congruent • Diagonals are perpendicular • Diagonals bisect one another • Diagonals bisect the angles A square is both a rectangle and a rhombus. • Ex. • AB is congruent to BC is congruent to CD is congruent to AD • AB is parallel to DC, AD is parallel to BC • <A, <B, <C, <D are all right angles (all congruent) • <ABC + <BCD = 180° • BD = AC • AC is perpendicular to BD • AC bisects BD, BD bisects AC • BD bisects <ABC and <ADC, AC bisects <BAD, <BCD

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