9-4 Arcs and Chords

Theorem Congruent arcs have congruent chords Congruent chords have congruent arcs. P A B C AB  BC if and only if AB  BC

Theorem

Congruent arcs have congruent chords

Congruent chords have congruent arcs.

Congruent arcs have Congruent diameters Congruent chords Congruent tangents Congruent secants 0 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Congruent diameters

Congruent chords

Congruent tangents

Congruent secants

What arcs are congruent? AB and DC BC and AB AE and AB BC and AE P A B C D E 10 11 8 3 5 7 0 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

AB and DC

BC and AB

AE and AB

BC and AE

Theorem If a diameter of a circle is  to a chord, then the diameter bisects the chord and its arc. F E D G DE  EF, DG  GF

Theorem

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

What is FD? 3 4 7 8 9 10 F E D G 3 5 O 0 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

3

4

7

8

9

10

Theorem Chords equally distant from the center are ___________

Theorem

Chords equally distant from the center are ___________

SPICSA Page 347 2-14,18 even

Page 347 2-14,18 even