Understanding Congruent Arcs and Chords in Geometry
This section of Geometry discusses significant theorems regarding chords and arcs within circles. Theorem 10.4 illustrates that two minor arcs within the same or congruent circles are congruent if their corresponding chords are congruent. Subsequent theorems explore properties of diameters and perpendicular bisectors of chords, including how to locate a point equidistant from various props in geometric configurations. These principles form the foundation for further exploration of circle geometry.
Understanding Congruent Arcs and Chords in Geometry
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Presentation Transcript
GEOMETRY: Chapter 10 10.2: Chords#2
Theorem 10.4 In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 664.
Ex.1: Answer:108o Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 665.
Bisecting Arcs Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 665.
Theorem 10.5 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 665.
Theorem 10.6 If one chord is a perpendicular bisector of another chord, then the first chord is a diameter. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 665.
Ex. 2: Three props are placed on a stage at points, P, Q, and R as shown. Describe how to find the location of a table so it is the same distance from each prop. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 665.
Ex. 2: Three props are placed on a stage at points, P, Q, and R as shown. Describe how to find the location of a table so it is the same distance from each prop. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 665.
Ex. 3: Images taken from: Geometry. McDougal Littell: Boston, 2007. P.666.
Ex. 3: Answer: 10; Theorem 10.5 Images taken from: Geometry. McDougal Littell: Boston, 2007. P.666.
Theorem 10.7 In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 666.
Ex. 4: Answer: 20 Images taken from: Geometry. McDougal Littell: Boston, 2007. P.666.
