1. Chapter 6: Properties of Circles
Objective:
Learn relationships among chords, arcs, and angles
Discover properties of tangent lines
Learn how to calculate the length of an arc

2. Match the terms to the examples
Circle terms we know:
Match the terms to the examples
Terms
1. Congruent Circles
2. Concentric Circles
3. Radius
4. Chord
5. Diameter E.
6. Tangent
7. Minor Arc
G. RQ
H. PRQ
I. PQR F.
8. Major Arc
9. Semicircle

3. Objective: Discover properties of chords
Chord Properties
Objective:
Discover properties of chords

4. Central Angle
  PQR,   PQS,   RST,
  QST, and    QSR are not
central angles of circle P.
     AOB,   BOC,   COD,   DOA, and   DOB are central angles of circle O.
A central angle has it vertex at the center of the circle

5. Inscribed Angle
  ABC,   BCD, and   CDE are inscribed angles.
  PQR,   STU, and
  VWX are not
inscribed angles.
An inscribed angle has its vertex on the circle and its sides are chords.

6. Chord Central Angles Conjecture B A
Construct large circle O
Construct to congruent chords and label AB and CD
Measure and compare angles the central angles of arcs AB & CD D C O
Chord Central Angles Conjecture
If two chords in a circle are congruent, then they determine two central angles that are ____________.
congruent
Chord Arcs Conjecture
If two chords in a circle are congruent, then their intercepted arcs are congruent.

7. Pg 310 #1-12, 16, 19-22 Perpendicular bisector of a Chord Conjecture
Construct the perpendicular for O to AB and O to CD. Label intersection M and N.
Measure AM, BM, CN, DN
Measure ON and OM D M N O B C
Perpendicular bisector of a Chord Conjecture
The perpendicular bisector of a chord passes through the _______ of the circle.
Perpendicular to a Chord Conjecture
The perpendicular from the center of a circle to a chord is the ___________ of the chord.
Chord distance to Center Conjecture
Two congruent chords in a circle are ___________ from the center of the circle.
equidistant
center
bisector
Pg 310 #1-12, 16, 19-22

8. Perpendicular to a Chord Conjecture
The perpendicular from the center of a circle to a chord is the ___________ of the chord.
bisector
Chord distance to Center Conjecture
Two congruent chords in a circle are ___________ from the center of the circle.
equidistant
Perpendicular bisector of a Chord Conjecture
The perpendicular bisector of a chord passes through the _______ of the circle.
center