1. 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

2. Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon
Number of Sides
Type of Polygon 3
Triangle 4
Quadrilateral 5
Pentagon 6
Hexagon 7
Heptagon 8
Octagon 9
Nonagon 10
Decagon 11
Unadecagon 12
Dodecagon n
n - gon

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

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

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

6. Chapter 6.4
Parallelogram – Quad. with 2 sets of parallel 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

7. 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

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

9. 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

10. 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

11. 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

12. Chapter 6.6 Notes
Quadrilateral Kite Parallelogram Trapezoid Rhombus Rectangle Isos. Trap. Square

13. 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

14. Rectangle Rhombus Square Kite Trapezoid
Property
Rectangle
Rhombus
Square
Kite
Trapezoid
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 ≌

15. Chapter 6.7
Area of a Square Postulate – the area of a square is the square of the length of its side, or A = s2 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

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

17. Area of a Trapezoid – ½ (b1 + b2). h Area of a Kite – ½ d1
Area of a Trapezoid – ½ (b1 + b2) * h Area of a Kite – ½ d1 * d2 Area of a Rhombus – ½ d1 * d2