Geometry 12 2 12 3 Arcs and Chords

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Geometry 12. 2 -12. 3 Arcs and Chords

Geometry 12. 2 -12. 3 Arcs and Chords

Goals o Identify arcs & chords in circles o Compute arc measures and angle

Goals o Identify arcs & chords in circles o Compute arc measures and angle measures 08 June 2021

Central Angle A 08 June 2021 An angle whose vertex is the center of

Central Angle A 08 June 2021 An angle whose vertex is the center of a circle.

Minor Arc C A 08 June 2021 Part of a circle. The measure of

Minor Arc C A 08 June 2021 Part of a circle. The measure of the central T angle is less than 180.

Semicircle C A D 08 June 2021 Half of a circle. The endpoints of

Semicircle C A D 08 June 2021 Half of a circle. The endpoints of the arc are the endpoints of a diameter. The central angle T measures 180.

Major Arc C A D 08 June 2021 T Part of a circle. The

Major Arc C A D 08 June 2021 T Part of a circle. The measure of the central angle is greater than 180.

Major Arc C BUT NOT A D 08 June 2021 T

Major Arc C BUT NOT A D 08 June 2021 T

Measuring Arcs o An arc has the same measure as the central angle. o

Measuring Arcs o An arc has the same measure as the central angle. o We say, “a central angle subtends an arc of equal measure”. A 42 42 C B Central Angle Demo 08 June 2021

Measuring Major Arcs o The measure of an major arc is given by 360

Measuring Major Arcs o The measure of an major arc is given by 360 measure of minor arc. A 42 42 D 08 June 2021 C B

Arc Addition Postulate Demonstration R T 08 June 2021 C A

Arc Addition Postulate Demonstration R T 08 June 2021 C A

What have you learned so far? o o o o o Page 607 Do

What have you learned so far? o o o o o Page 607 Do problems 3 – 8. Answers… 3) 4) 5) 6) 7) 8) 08 June 2021 Q T 40 R 60 S P 120

Subtending Chords A O C 08 June 2021 Chord AB subtends AB. B Chord

Subtending Chords A O C 08 June 2021 Chord AB subtends AB. B Chord BC subtends BC.

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08 June 2021

Theorem 12. 4 o Two minor arcs are congruent if and only if corresponding

Theorem 12. 4 o Two minor arcs are congruent if and only if corresponding chords are congruent. 08 June 2021

Theorem 12. 4 B A C D 08 June 2021

Theorem 12. 4 B A C D 08 June 2021

Example Solve for x. 120 (5 x + 10) 5 x + 10 =

Example Solve for x. 120 (5 x + 10) 5 x + 10 = 120 5 x = 110 x = 22 08 June 2021

Theorem 12. 5 o If a diameter is perpendicular to a chord, then it

Theorem 12. 5 o If a diameter is perpendicular to a chord, then it bisects the chord and the subtended arc. 08 June 2021

Example Solve for x. 52 2 x 08 June 2021 2 x = 52

Example Solve for x. 52 2 x 08 June 2021 2 x = 52 x = 26

Theorem 12. 6 o If a chord is the perpendicular bisector of another chord,

Theorem 12. 6 o If a chord is the perpendicular bisector of another chord, then it is a diameter. Diameter 08 June 2021

Theorem 12. 7 o Two chords are congruent if and only if they are

Theorem 12. 7 o Two chords are congruent if and only if they are equidistant from the center of a circle. 08 June 2021

The red wires are the same length because they are the same distance from

The red wires are the same length because they are the same distance from the center of the grate. 08 June 2021

Example 16 Solve for x. 4 x – 2 = 16 4 x =

Example 16 Solve for x. 4 x – 2 = 16 4 x = 18 2 4 x – x = 18/4 x = 4. 5 08 June 2021

Summary o Chords in circles subtend major and minor arcs. o Arcs have the

Summary o Chords in circles subtend major and minor arcs. o Arcs have the same measure as their central angles. o Congruent chords subtend congruent arcs and are equidistant from the center. o If a diameter is perpendicular to a chord, then it bisects it. 08 June 2021

Practice Problems 08 June 2021

Practice Problems 08 June 2021

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