Chapter 6.1 Notes Polygon – is a simple, closed figure made with straight lines. vertex vertex side side Convex – has no indentation Concave – has an indentation

Number of SidesType of Polygon 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon n n - gon

Equilateral – Equiangular – Regular – Diagonal – Interior Angles of a Quadrilateral – sum of the interior angles of in Quad. is _ _ _.

Chapter 6.2 Notes Thm – Opposite sides are ≌ in a parallelogram Thm – Opposite ∠’s are ≌ in a parallelogram Thm – Consecutive ∠’s are supp. in a parallelogram Thm – Diagonals bisect each other in a parallelogram

Chapter 6.3 Notes The five ways of proving a quadrilateral is a parallelogram. 1) 2) 3) 4) 5)

Chapter 6.4 Parallelogram – Quad. with 2 sets of parallelogram sides Rhombus – is a parallelogram with 4 ≌ sides Rectangle – is a parallelogram with 4 rt. angles Square - is a parallelogram with 4 ≌ sides and four right angles

Thm – a parallelogram is a rhombus if and only if its diagonal are perpendicular Thm – a parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles Thm - a parallelogram is a rectangle if and only if its diagonals are congruent

Chapter 6.5 Notes Trapezoid – is a quadrilateral with exactly one pair of parallel sides. Isosceles Trapezoid – is a trapezoid with congruent legs

Thm – If a trapezoid is isosceles, then each pair of base angles is congruent Thm – If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid. Thm – a trapezoid is isosceles if and only if its diagonals are congruent

Midsegment Thm for Trapezoids – the midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases

Thm – If a quadrilateral is a kite, then its diagonals are perpendicular. Thm - If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent

Chapter 6.6 Notes Quadrilateral KiteParallelogramTrapezoid Rhombus RectangleIsos. Trap. Square

Ways to prove a Quad. is a Rhombus 1) Prove it is a parallelogram with 4 ≌ sides 2) Prove the quad. is a parallelogram and then show diagonals are perpendicular 3) Prove the quad. is a parallelogram and then show that the diagonals bisect the opposite angles

PropertyRectangleRhombusSquareKiteTrapezoid Both pairs of opp. sides are II Exactly 1 pair of opp. sides are II All ∠’s are ≌ Diagonals are ⊥ Diagonals are ≌ Diagonals bisect each other Both pairs of opp. Sides are ≌ Exactly 1 pair of opp. sides are ≌ All sides are ≌

Chapter 6.7 Area of a Square Postulate – the area of a square is the square of the length of its side, or A = s 2 Area Congruence Postulate – if 2 polygons are ≌, then they have the same area Area Addition Postulate – the area of a region is the sum of the areas of its nonoverlapping parts

Area of a Rectangle – b * h or l * w Area of a Parallelogram – b * h Area of a Triangle – ½ b * h

Area of a Trapezoid – ½ (b 1 + b 2 ) * h Area of a Kite – ½ d 1 * d 2 Area of a Rhombus – ½ d 1 * d 2