Name: _ Date: _ Period: _
10.6 Secants, Tangents, and Angle Measures
Tangent: _
Secant: _
* Chords and diameters are special types of secants
Intersection in the
Interior of the Circle
Intersection on the Circle
mCBD =
1
mCED
2
Intersection in the
Exterio
Name: _ Date: _ Period: _
10.7 Special Segments in a Circle
If two chords intersect in a circle, then the products of the measures of the segments of the chord are
equal.
Example: If
,
, and
, find
.
If two secants are drawn from the same exterior point,
Name: _ Date: _ Period: _
11.1 Area of Parallelograms
Recall
Parallelogram: a quadrilateral with both pairs of opposite sides parallel
Base: _
Altitude: _
Height: _
Area of a Parallelogram
A = bh
Examples: Find the perimeter and area of each parallelogram
Name: _ Date: _ Period: _
11.2 Areas of Triangles, Trapezoids, and Rhombi
Area of a Triangle
Area of a Trapezoid
Area of a Rhombus
b1
d1
d2
h
h
b2
b
Examples: Find the area of each figure.
1.
2.
4.
5.
3.
6.
7. Find the area of trapezoid FGHJ if F ( 1, 8 )
Name: _ Date: _ Period: _
11.3 Areas of Regular Polygons and Circles
Area of a Regular Polygon
1
A = Pa where P is the perimeter of the polygon and a is the apothem
2
Apothem a perpendicular segment drawn from the center of a
regular polygon to a side
Exa
Name: _ Date: _ Period: _
10.1 Circles and Circumference
Circle: a group of points in a plane equidistant from a given point
Center: a point located in the middle of a circle
* used to name a circle, example:
Parts of a Circle
1. Chord: any segments whose
Name: _ Date: _ Period: _
10.2 Angles and Arcs
Central Angle: an angle whose vertex is the center of the circle and whose legs are radii
* The sum of all central angles of a circle is
* Example:
Types
Types of Arcs
Minor Arc
Major Arc
D
A
Figure
Semicircl
Name: _ Date: _ Period: _
10.3 Arcs and Chords
Theorem: In a circle or two congruent circles, two minor arcs are congruent if and only if their
corresponding chords are congruent.
Example: If
, then
.
If
, then
.
Inscribed Polygon: a polygon where each of
Name: _ Date: _ Period: _
10.4 Inscribed Angles
Inscribed Angle: an angle that has its vertex on the circle and chords as sides
* Example:
* Vertex B is on the circle
*
and
are chords
*
is the arc intercepted by
Inscribed Angle Theorem
If an angle is insc
Name: _ Date: _ Period: _
10.5 Tangents
Tangent: a line that intersects a circle at exactly one point
* Example:
Point of Tangency: the point of intersection of a tangent and a circle
* Example:
Theorem: If a line is tangent to a circle, then it is perpen