Transcript Chapter 6.1 Notes - Illini West High School

Chapter 6.1 Notes
Polygon – is a simple, closed figure made with
straight lines.
vertex
side
vertex
side
Convex – has no indentation
Concave – has an indentation
Number of Sides
Type of Polygon
3
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n - gon
4
5
6
7
8
9
10
12
n
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
Kite
Parallelogram
Rhombus Rectangle
Square
Trapezoid
Isos. Trap.
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
Property
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 ≌
Rectangle
Rhombus
Square
Kite
Trapezoid
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
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 (b1 + b2) * h
Area of a Kite – ½ d1 * d2
Area of a Rhombus – ½ d1 * d2