11.6 Areas of Regular Polygons
The center of the polygon
radius of the polygon are
the center and the radius
of its circumscribed circle.
The distance from the center
to any side of the polygon is
called the apothem of the polygon.
A central angle
11.4 Circumference and Arc Length
Theorem 11.8 Circumference of a Circle:
The circumference, C, of a circle is
C = 2r or C = d
where d is the diameter and r is the radius.
1. The circumference of a circle with radius 6cm
Circumference
8.5 Properties of
Trapezoids and Kites
Assignment
Handout
Trapezoids
A trapezoid is a
quadrilateral with exactly
one pair of parallel sides.
The parallel sides are
called the bases.
A trapezoid has two pairs
of base angles. In
trapezoid ABCD, D and
C are
8.4 Properties of
Rhombuses, Rectangles
and Squares
Assignment
Handout
Rectangles
A rectangle
is a parallelogram with four
right angles.
Rectangle Corollary: The quad. is a
rectangle if and only if it has four right
angles.
Rectangles
Since rectangles
8.3 Showing a Quad. is a
Use the following theorems to prove that a quadrilateral
is a parallelogram.
Theorem 8.7 If both pairs of opposite sides of a quad.
are congruent, then the quad. is a .
8.2 Use Proper,es of Parallelograms
Assignment: Practice C
Deni,on:
A parallelogram is a quadrilateral with
both pairs of opposite sides parallel.
Proper,es of Every Parallelogram:
Theorem 8.3 If a quad. is a ,
8.1 Find Angle Measures
in Polygons
Diagonal: Connects two nonconsecutive vertices (ex: AC)
A
E
B
C
D
Polygon
# of Sides
# of Triangles
created by
nonintersecting
diagonals
Sum of
Measures
of Interior
angles
Sum of
Measures
of Interior
angles
1
1180
180
4
7.7 Solving Right Triangles
Assignment: Handout for 7.7
Using Inverse Trig Ra<os to nd angles
Inverse sine: If sin A = s, then sin
1 s = m<A

1
Inverse cosine: If cos A = s, then cos s = m<A
Inverse
7.5, 7.6 Trigonometric Ra3os
Assignment: Handout for 7.5 and 7.6
Finding Trig Ra3os
A trigonometric ra3o is a ra3o of the
lengths of two sides of a right triangle.
Abbrevia3ons: Sine sin, cosine cos,
tange
7.3 Use Similar Triangles
7.3 #19, #3139
Do Now: The Geometric Meanwithout triangles! REVIEW
Find the Geometric mean between the two numbers!
1. 8 and 12
2. 2a and 4a
8x
=
x2 12
x = 96
x = 96
x=4 6
2a
x
=
x 4a
x 2 = 8a 2
x = 8a 2
x = 2a 2
Section 7.3
U
7.2 Converse of Pythagorean
Theorem
Assignment
7.1Extra Practice Worksheet #712,1416,1928, 31,32
7.2 Worksheet #1,3,4,8,11,13,15,16,18
*Special Note: Always put c, the longest given side, on the left
side of the test equation!
Example 5:
7.1 Pythagorean Theorem
Practice C
#s 2,4,6,8,18,23,24,
2630,32,33,34
Pythagoras
Lived in southern Italy
during the sixth century
B.C.
Considered the first true
mathematician
Used mathematics as a
means to understand the
natural world
First to teach tha
DO NOW
Draw an obtuse scalene triangle.
Find the largest angle and longest side and mark them red.
Find the smallest angle and shortest side and mark them blue.
What do you notice?
Example 1
Assignment:
Section 5.5
Practice C #115, Challenge #15.