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6.1 Polygons
EQ: What are polygons and what are some types of polygons?
Polygon: a plane figure that is:
formed by 3 or more segments called sides
each side intersects exactly 2 other sides, one at each endpoint
Vertex: each endpoint of a side
State whether the figure is a polygon. If it is not, then explain why not?
A list of named polygons can be found on page 322 in your textbook.
Convex polygon: a polygon which does not “cave in”
Concave polygon: a polygon which “caves in” on at least one side
Equilateral polygon: all of its sides are congruent
Equiangular polygon: all of its interior angles are congruent
Regular polygon: both equilateral and equiangular
Diagonal: a segment that joins two nonconsecutive vertices.
Theorem: the sum of the interior angles of a quadrilateral is 360.
m<1 +m<2 +m<3 + m<4 = 360
page 325: 1 – 30, 37 – 39, 41 – 46.
6.2 Properties of Parallelograms
EQ: What properties are true about parallelograms?
Parallelogram: a quadrilateral with both pairs of opposite sides parallel.
Theorems about Parallelograms:
If a quadrilateral is a parallelogram, then its
1. opposite sides are congruent
2. opposite angles are congruent
3. consecutive angles are supplementary
4. diagonals bisect each other
Page 333: 1 – 37, 59 – 64 all
A
D
B
C
6.3 Proving Quadrilaterals are Parallelograms
EQ: What information is needed to prove quadrilaterals are parallelograms?
Theorems about Parallelograms
If both pairs of opposite sides of a quadrilateral are congruent . . .
If both pairs of opposite angles of a quadrilateral are congruent . . .
If an angle of a quadrilateral is supplementary to both its consecutive angles . . .
If the diagonals of a quadrilateral bisect each other . . .
If one pair of opposite sides of a quadrilateral are congruent and parallel. . .
then the quadrilateral is a parallelogram.
A
D
Page 342: 1 – 28
B
C
6.4 Rhombuses, Rectangles, and Squares
EQ: What attributes distinguish rhombuses, rectangles, and squares?
Rhombus: a parallelogram with 4 congruent sides
Rectangle: a parallelogram with 4 right angles
Square: a parallelogram with 4 congruent sides and 4 right angles
Venn Diagram of Parallelograms
Parallelograms
Rhombuses
Squares
Rectangles
Theorems
A parallelogram is a rhombus
if and only if its diagonals are perpendicular
if and only if each diagonal bisects a pair of opposite angles
A parallelogram is a rectangle if and only if its diagonals are congruent.
Page 351: 1 – 43
6.5 Trapezoids and Kites
EQ: How are trapezoids and kites different from parallelograms?
Trapezoid: a quadrilateral with exactly one pair of parallel sides.
Bases: the two parallel sides in a trapezoid.
Legs: the two nonparallel sides in a trapezoid.
Isosceles trapezoid: a trapezoid with two congruent legs.
Base angles: the 2 sets of angles formed at each base.
Midsegment of a trapezoid: the segment that connects the midpoints of the legs.
The length of the midsegment is ½ the sum of the bases.
A
E
D
B
F
C
EF = ½ (AB + CD)
EF = ½ ( + )
EF = ½ (
)
EF =
Kite: a quadrilateral that has 2 pairs of consecutive congruent sides, but opposite
sides are not congruent.
Theorems: If a quadrilateral is a kite . . .
then its diagonals are perpendicular
then exactly one pair of opposite angles are congruent.
Page 359: 1 – 33
2nd, 3rd, and 5th periods: omit 28 – 30
6.6 Special Quadrilaterals
EQ: What are some other special quadrilaterals?
Quadrilaterals
Kite
Parallelogram
Rhombus
Rectangle
Square
Page 367: 2 – 24, 30 – 35
Trapezoid
Isosceles Trapezoid
Parallelogram
Rhombus
Rectangle
Square