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Bronx High School of Science
Ms. Abbott
Mathematics Department
M$4
Unit 4: Quadrilaterals
DEFINITIONS
 A parallelogram is a quadrilateral in which both pairs of opposite sides are
parallel.
 A rectangle is a parallelogram with one right angle.
 A rhombus is a parallelogram with two adjacent sides congruent.
 A square is a rectangle with two adjacent sides congruent.
 A trapezoid is a quadrilateral that has one and only one pair of sides parallel.
 An isosceles trapezoid is a trapezoid with congruent legs.
 The parallel sides of a trapezoid are bases (upper and lower).
 The non-parallel sides of a trapezoid are legs.
 In a trapezoid, the pair of angles that have one side as a base are a pair of
base angles (a trapezoid has 2 pairs, one pair for each base).
POSTULATES
THEOREMS and COROLLARIES
 The opposite sides of a parallelogram are congruent.
 The opposite angles of a parallelogram are congruent
 The diagonals of a parallelogram bisect each other.
 In a quadrilateral, if both pairs of opposite sides are congruent, the
quadrilateral is a parallelogram.
 In a quadrilateral, if one pair of opposite sides is both congruent and parallel,
the quadrilateral is a parallelogram.
 In a quadrilateral, if the diagonals bisect each other, the quadrilateral is a
parallelogram.
 In a quadrilateral, if both pairs of opposite angles are congruent, the
quadrilateral is a parallelogram.
 A rectangle has all right all right angles.
 The diagonals of a rectangle are congruent.
 All sides of a rhombus are congruent.
 The diagonals of a rhombus bisect the angles.
 If a parallelogram has congruent diagonals, then it is a rectangle.
 If a quadrilateral is equiangular, then it is a rectangle.
 If a parallelogram has perpendicular diagonals, then it is a rhombus.
 If a parallelogram has a diagonal that bisects the angles, then it is a rhombus.
 If a quadrilateral is equilateral, then it is a rhombus.
 If a rhombus has one right angle, then it is a square.
 A trapezoid is isosceles if and only if a pair of base angles is congruent.
 A trapezoid is isosceles if and only if the diagonals are congruent.
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