Quadrilaterals Parallelogram Square Rectangle Rhombus Kite Trapezoid Isosceles Trapezoid A shape with 4 sides A shape with two sets of parallel sides A shape with four congruent sides and four right angles A shape with four right angles A shape with four congruent sides A shape with adjacent congruent sides A shape with at least one set of parallel sides A trapezoid with at least one pair of congruent sides What makes a parallelogram? 2 sets of opposite parallel sides Is it a parallelogram? Tell how you know each shape is a parallelogram. 1 pair of parallel and congruent sides 1 angle is supplementary to both adjacent angles diagonals bisect each other 2 sets of opposite congruent angles 2 sets of opposite congruent sides Write 10 conditional statements. If it is a _____________, then it is a _____________. square rectangle If it is a _____________, then it is a _____________. rectangle square could be __ 40° 140° 140° Solve the parallelogram Use what you know about parallelograms to solve for each variable. 55° y° 4x+2 5x-1 23 5x+3 8 3x+2 (5x+5)° 3x 12 6x y (4x-8)° (9x-7)° (2y)° 3x+5 5x+1 4y-1 4x+7 Show that Each is a Parallelogram Plot each set of points and use the indicated property to show that the shape is a parallelogram (2, -1), (1, 3), (6, 5), (7, 1) (-2, -4), (1, 2), (2, 10), (-1, 4) Opposite sides are parallel Opposite sides are congruent Diagonals bisect each other (-2, 8), (3, 7), (6, 2), (1, 3) (-4, 7), (3, 0), (2, -5), (-5, 2) One pair of sides is parallel and congruent Properties of Squares Properties of a Rectangle Properties of a parallelogram

Four right angles

Diagonals congruent Properties

of a Rhombus Properties of parallelogram

Diagonals are perpendicular

Four congruent sides Solve each Square Solve the Rectangle Solve

each Rhombus Properties of a parallelogram

Four right angles

Diagonals are congruent and perpendicular

Four congruent sides 3x+5 4x+1 (6x+42)° 6 3x (10x+10)° 5x-3 4x+3 3x+2 4x-1 5 6x 13 6x+3 8x+1 5x+35 2x+5 2x+1 3 4 Solve the Kite Properties of a Kite Adjacent sides congruent

one pair of congruent angles

diagonals are perpendicular Properties of a Trapezoid Midsegment is the average of the bases

One set of parallel sides Solving a Trapezoid Properties of an Isosceles Trapezoid properties of a trapezoid

diagonals are congruent

one pair of congruent sides Solving an Isosceles Trapezoid 2x+1 3x-3 5y-8 3y+2 (4x+15)° (5x-10)° (2x-5)° y° (7x+20)° (7x+5)° (10x+85)° 3y° 2x x+3 8 4x+2 12 30° (3x+30)° 2y 5y-1 5x-3 4x+1 8x+5 3x-6 x+2 (5x+10)° (4x+35)° y°

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# Quadrilaterals

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