8-4 Trigonometry Continued
What if you wanted to know the measure of the acute angles of a right triangle
and you only had the side lengths?
What about the measure of angles D and E?
Example 1 Solve the right triangle. Round angle measurements to the near
8-7 Vectors
Some quantities are described by a real number known as a scalar, which describes the
magnitude or SIZE of the quantity.
Other quantities are described by a _. This describes both the
_ and _ of the quantity.
Example:
A vector can be represent
IP 17
Name _
Geometry
Date _
Honors
Square ACBD is inscribed in a circle with center E.
Find the following measurements. Give the exact answers.
BD = 6, CG = 3 + 3 3
CD = _
GJ = _
FB = _
ED = _
GB = _
CJ = _
CF = _
JE = _
mFJE = _
FJ = _
EA = _
mAFJ = _
J
10-2 Arc Length
GSP Investigation
In the EDIT menu, go to Preferences and change Precision to tenths for Angle,
Distance and Other.
Constructing Arcs
Construct a circle and two points on the circle.
To construct a minor arc corresponding to the two points
WS 10-2.2
Name _
Honors Geometry
Date _
A circle with radius r is inscribed in a square and circumscribed about a regular hexagon.
r
1. What are the perimeters of the square and hexagon in terms of r?
2. Is the circumference of the circle greater or less
10-3 Arcs and Chords
Recall: Biconditional Statement
_
_
_
_
Intercepted Arc
_
_
_
For circle A, name the arc intercepted by the following:
E
DE
BAC
DF
EDF
D
F
A
B
C
If a segment, ray or line divides an arc into two congruent arcs, then it
bisects the a
10-3 Arcs and Chords
Recall: Biconditional Statement
_
_
_
_
Intercepted Arc
_
_
_
For circle A, name the arc intercepted by the following:
E
DE
BAC
DF
EDF
D
F
A
B
C
If a segment, ray or line divides an arc into two congruent arcs, then it
bisects the a
10-4 Inscribed Angles
Inscribed Angle an angle whose vertex is on
_
and contains _
GSP Investigation
In the EDIT menu, go to Preferences and change Precision to tenths for Angle,
Distance and Other.
Investigation #1
1.
2.
3.
Construct a circle with center
WS 10-5.2
Name _
Honors Geometry
Date _
Examples
Mixed
1. Find the coordinates of the center of the circle.
B (3,11)
A (-14,4)
C (11,-1)
suu
r
suu
r
AT is tangent to circle P. Find the equation of AT .
2.
y
A (3 , 9 )
T
x
P
2
3. In Circle O below, mCBA =
Name _
Honors Geometry
Date _
Proofs
Circle
Complete each of the following proofs. (5 pts each)
Due the day of the Chapter 10 Test.
o #1 6 (Section 10-3)
o #7 13 (Section 10-4)
o #14 16 (Section 10-5)
1.
Given: Circle P,
FG JH
Prove: FG JH
G
P
H
F
J
2.
10-8 Equations of Circles
Recall: A circle is the set of all points equidistant from a given point (the center).
We can write the equation of a circle, just like we can write the equation of a line
( y = mx + b or ax + by = c ).
To do this, lets look at t
10-7 Special Segments in a Circle
Chord Segments
Secant Segment
External Secant Segment
Tangent Segment
GSP Investigation
In the EDIT menu, go to Preferences and change Precision to tenths for Angle,
Distance and Other.
Investigation #1
1. Construct C
Ch.11 Area (Part I)
Height triangle =
_
Parallelogram/Trapezoid =
_
_
_
Formulas
Triangle
Parallelogram
Trapezoid
Rhombus
Kite
Derivation of Rhombus and Kite Formulas
G
C
B
F
J
E
D
A
I
Herons Formula for finding the area of a Triangle
Example:
A triangle
7-5 Parts of Similar Triangles
GSP Investigation
In the EDIT menu, go to Preferences and change Precision to hundredths for Angle,
Distance and Other.
Investigation #1 Save this sketch as LastName_PartsSimilarTriangles
1.)
Construct two segments AB and CD
WS 8-4.3
Name _
Date _
Honors Geometry
Challenging Trig Problems
1. If AB = 10, find the value of h.
(Hint: use a system of two equations with variables x and h)
D
h
40
A
10
54
B
x
2. An airplane is flying at an elevation of 5150 ft. directly above a st