Geometry Lesson 61 Pg' 306

1
GeometryLesson 6-1 Pg. 306

• Chords of a Circle

2
See Page 306 in Geom. Book

• Name all the parts of a circle matching.

3
Definitions

• Central Angle Is an angle whose vertex is the
  center of the circle and the sides are the radii.
• Inscribed Angle Is an angle whose vertex is on
  the circle and whose sides are chords of the
  circle.

4
Theorem 6-1

• Equal chords in a circle determine equal central
  angles.
• ?APB ?XPY
• AB XY

X
A
P
Y
B
5
Theorem 6-2

• In the same circle or in equal circles,
• 1. Equal chords have equal arcs
• 2. Equal arcs have equal chords
• Proof on next slide.

6
Proof of Theorem 6-2
P

• Given Equal circles O and P. AB CD.
• Prove AB CD
• Statement
  Reason
• 1. Draw OA, OB, PC, PD 1. Through any
  two pts. exactly
• 
  one line can be drawn.
• 2. OA PC OB PD 2. Radii of
  equal circles are equal.
• 3. Equal circles O and P. AB CD. 3.
  Given
• 4. ?AOB ? ?CPD 4. SSS
• 5. ?O ?P 5.
  CPCTE
• 6. AB ?O CD ?P 6. The
  measure of a minor arc is equal to
• 
  the measure of its central angle.
• 7. AB CD 7.
  Substitution Property

D
C
O
A
B
7
Theorem 6-3

• A diameter that is perpendicular to a chord
  bisects the chord and its arc.
• AX BX
• AY BY

Z
ZY ? AB
P
X
A
B
Y
8
Theorem 6-4

• In the same circle or in equal circles,
• 1. Equal chords are equally distant from
• the center of the circle.
• 2. Chords equally distant from the center
• are equal.

P