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S. McMurtrie
NAME _____________________________
The Unit Organizer
4 BIGGER PICTURE
DATE ______________________________
Geometry
2
LAST UNIT/Experience
Quadrilaterals
8
UNIT SCHEDULE
1
3
CURRENT UNIT
Chapter 10: Properties of Circles
5 UNIT MAP
10.1 Homework
G.1.1.1.1
10.2 Homework
G.1.1.1.2
10.3 Homework
10.1 Use
Properties of
Tangents
M11.C.1.1.1
Find the lengths of segments or
arcs, and the measures of arcs and
angles in a circle
G.1.1.1.3
G.1.1.1.2
10.5 Homework
10.2 Find Arc
Measures
M11.C.1.1.2
G.1.1.1.2
10.6 Homework
G.1.1.1.3
Rev Review Worksheet
7
M11.A.3.2.1
10.3 Apply
Properties of
Chords
10.4 Use
Inscribed
Angles and
Polygons
10.5 Apply Other
Angle
Relationships in
Circles
M11.A.3.2.1; M111.C.1.1.1;
M11.C.1.1.2
M11.C.1.1.2
How can you verify that a segment is tangent to a circle? (2.9)
How do you find the measure of an arc of a circle? (2.9)
How can you tell if two chords in a circle are congruent? (2.9)
How do you find the measure of an inscribed angle? (2.9)
How do you find the measure of the angle formed by two chords that intersect inside the
circle? (2.9)
What are some properties of chords, secants, and tangents to a circle? (2.9)
What do you need to know to write the standard equation of a circle? (2.8; 2.9)
(13.1.11B)
cause/effect
examples
steps
6
UNIT
RELATIONSHIPS
UNIT SELF-TEST
QUESTIONS
Test Chapter 10 Test
10.6 Find
Segment Lengths
in Circles
Pages 648-712
Quiz Quiz 10.1-10.3
10.4 Homework
NEXT UNIT/Experience
Measuring Length and Area
NAME _____________________________
The Unit Organizer
Chapter 10: Properties of Circles
DATE ______________________________
9 EXPANDED UNIT MAP
10.6 Find
Segment Lengths
in Circles
10.1 Use
Properties of
Tangents
Circle – the set of all points in a
plane that are equidistant from a
given point
Center – the given point
Radius – a segment from the
center to the outside of the circle
Chord – a segment whose
endpoints are on the circle
Diameter – a chord that contains
the center of the circle
Secant – a line that intersects a
circle at two points
Tangent – a line that intersects the
circle in exactly one point
Point of tangency – the
intersection point of the tangent
and the circle
In a plane, a line is tangent to a
circle if and only if the line is
perpendicular to a radius of the
circle at its endpoint on the circle.
Tangent segments from a common
external point are congruent.
NEW
UNIT
SELF-TEST
QUESTIONS
10
10.2 Find Arc
Measures
Central angle – an angle
whose vertex is the center
of the circle
Minor arc – an arc less
than 180
Major arc – an arc
greater than 180
Semicircle – an arc
measuring 180
The measure of an arc is
equal to the measure of
its central angle.
Arc Addition Postulate
– The measure of an arc
formed by two adjacent
arcs is the sum of the
measures of the two arcs.
Congruent circles –
circles with the same
radius
Congruent arcs – arcs
with the same measure
from congruent circles
Find the lengths of segments or
arcs, and the measures of arcs
and angles in a circle
Pages 648-712
10.3 Apply
Properties
of Chords
In the same circle, or in
congruent circles, two minor
arcs are congruent if and only
if their corresponding chords
are congruent.
If one chord is a perpendicular
bisector of another chord, then
the first chord is a diameter.
If a diameter of a circle is
perpendicular to a chord, then
the diameter bisects the chord
and its arc.
In the same circle, or in
congruent circles, two chords
are congruent if and only if
they are equidistant from the
center.
10.4 Use
Inscribed
Angles and
Polygons
Inscribed angle – an angle whose
vertex is on the circle; is equal to
half of its intercepted arc
Intercepted arc – the portion of
the circle between the sides of an
angle
A right triangle is inscribed in a
circle if and only if its hypotenuse
is the diameter of the circle.
A quadrilateral can be inscribed in
a circle if and only if its opposite
angles are supplementary.
10.5 Apply Other
Angle
Relationships in
Circles
If a tangent and a chord intersect
at a point on the circle, then the
measure of each angle formed is
one half the measure of its
intercepted arc.
If two chords intersect inside of a
circle, then the measure of each
interior angle is one half the sum
of the measures of the arcs
intercepted by the angle and its
vertical angle.
If a tangent and a secant, two
tangents, or two secants intersect
outside of a circle, then the
measure of the angle formed is one
half the difference of the measures
of the intercepted arcs.
How can you graph a circle on a graphing calculator?
How do you find the lengths of segments that fall outside of the circle?
What is a common tangent?
What is the difference between the tangent of a circle and the tangent ratio in a triangle?
Segments of Chords Theorem – If
two chords intersect in the interior of
a circle, then the product of the
lengths of the segments of one chord
is equal to the product of the lengths
of the segments of the other chord.
Secant segment – a segment that
contains a chord of a cricel and has
exactly one endpoint outside of the
circle
External segment – the part of a
secant segment that is outside of the
circle.
Segments of Secants Theorem - If
two secant segments share the same
endpoint outside of a circle, then the
product of the lengths of one secant
segment and its external segment
equals the product of th elenghts of
the other secant segment and its
external segment.
Segments of Secants and Tangents
Theorem – If a secant segment and
a tangent segment share an endpoint
outside of a circle, then the product
of the lengths of the secant segment
and its external segment equals the
square of the length of the tangent
segment.