Download presentation
Presentation is loading. Please wait.
Published byPenelope Ramsey Modified over 9 years ago
2
Geometry Arcs and Chords
3
September 13, 2015 Goals Identify arcs & chords in circles Compute arc measures and angle measures
4
September 13, 2015 Central Angle An angle whose vertex is the center of a circle. A
5
September 13, 2015 Minor Arc Part of a circle. The measure of the central angle is less than 180. A C T
6
September 13, 2015 Semicircle Half of a circle. The endpoints of the arc are the endpoints of a diameter. The central angle measures 180. A C T D
7
September 13, 2015 Major Arc Part of a circle. The measure of the central angle is greater than 180. A C T D
8
September 13, 2015 Major Arc BUT NOT A C T D
9
September 13, 2015 Measuring Arcs An arc has the same measure as the central angle. We say, “a central angle subtends an arc of equal measure”. 42 A B C Central Angle Demo
10
September 13, 2015 Measuring Major Arcs The measure of an major arc is given by 360 measure of minor arc. 42 A B C D
11
September 13, 2015 Arc Addition Postulate R A C T Postulate Demonstration
12
September 13, 2015 What have you learned so far? Page 607 Do problems 3 – 8. Answers… 3) 4) 5) 6) 7) 8) P Q R S T 120 60 40
13
September 13, 2015 Subtending Chords A B O C Chord BC subtends BC. Chord AB subtends AB.
14
September 13, 2015
15
Theorem 12.4 Two minor arcs are congruent if and only if corresponding chords are congruent.
16
September 13, 2015 Theorem 12.4 A B C D
17
September 13, 2015 Example 120 (5x + 10) Solve for x. 5x + 10 = 120 5x = 110 x = 22
18
September 13, 2015 Theorem 12.5 If a diameter is perpendicular to a chord, then it bisects the chord and the subtended arc.
19
September 13, 2015 Example 52 2x Solve for x. 2x = 52 x = 26
20
September 13, 2015 Theorem 12.6 If a chord is the perpendicular bisector of another chord, then it is a diameter. Diameter
21
September 13, 2015 Theorem 12.7 Two chords are congruent if and only if they are equidistant from the center of a circle.
22
September 13, 2015 The red wires are the same length because they are the same distance from the center of the grate.
23
September 13, 2015 Example 16 4x – 2 Solve for x. 4x – 2 = 16 4x = 18 x = 18/4 x = 4.5
24
September 13, 2015 Summary Chords in circles subtend major and minor arcs. Arcs have the same measure as their central angles. Congruent chords subtend congruent arcs and are equidistant from the center. If a diameter is perpendicular to a chord, then it bisects it.
25
September 13, 2015 Practice Problems
Similar presentations
© 2024 SlidePlayer.com Inc.
All rights reserved.