Lesson 6.2 Properties of Chords

1
Lesson 6.2 Properties of Chords
Objective Discover properties of chords of a
circle

• Homework Lesson 6.2/1-12

2

• What is a chord?
• A chord is a segment with endpoints on a circle.
  
• Any chord divides the circle into two arcs.
• A diameter divides a circle into two semicircles.
  
• Any other chord divides a circle into a minor arc
  and a major arc.

3
Chord Arcs Conjecture

• In the same circle, two minor arcs are congruent
  if and only if their corresponding chords are
  congruent.

 
IFF
 
G
and
IFF
 
 
and
 
4
(No Transcript)
5
Perpendicular Bisector of a Chord Conjecture

• If a diameter of a circle is perpendicular to a
  chord, then the diameter bisects the chord and
  its arc.

H
 
 
6
is a diameter of the circle.
7
Perpendicular Bisector to a Chord Conjecture

• If one chord is a perpendicular bisector of
  another chord,
• then the first chord passes through the center of
  the circle and is a diameter.

is a diameter of the circle.
8
If one chord is a perpendicular bisector of
another chord, then the first chord is a
diameter.
9
Ex. 4 Using Chord Arcs Conjecture
(x 40)
D
 
2x
C
A
B
2x x 40
x 40
10
Ex. 5 Finding the Center of a Circle

• Perpendicular bisector to a chord can be used to
  locate a circles center as shown in the next few
  slides.
• Step 1 Draw any two chords that are not
  parallel to each other.

11
Ex. 5 Finding the Center of a Circle

• Step 2 Draw the perpendicular bisector of each
  chord.
• These are the diameters.

12
Ex. 5 Finding the Center of a Circle

• Step 3 The perpendicular bisectors intersect at
  the circles center.

13
Chord Distance to the Center Conjecture

•  

14
AB ? CD if and only if EF ? EG.
15
Ex. 7

• AB 8 DE 8, and CD 5. Find CF.

16
 
 
17

•  

18

•  

(x 40)
D
2x
 
2x x 40
x 40
19
Ex.4 Solve for the missing sides.
 
A
7m
C
3m
D
BC AB AD
7m 14m 7.6m
B
20

•  

21
Ex.6 QR ST 16. Find CU.
 
 
x 3
22
Ex 7 AB 8 DE 8, and CD 5. Find CF.
CG CF
 
 
 
 
CG 3 CF
23

• Ex.8 Find the length of
• Tell what theorem you used.

BF 10
Diameter is the perpendicular bisector of the
chord Therefore, DF BF
24
Ex.9 PV PW, QR 2x 6, and ST 3x 1. Find
QR.
 
 
 
 
 
Congruent chords are equidistant from the center.
25

•  

Congruent chords intercept congruent arcs
 
26
Ex.11
Congruent chords are equidistant from the center.
 
 
 
 
 
27
(No Transcript)