Chords and Arcs Unit 12 Lesson 2 CHORDS

Chords and Arcs Unit 12 Lesson 2

CHORDS AND ARCS Students will be able to: Understand the postulates and theorems on arcs and chords and solve problems arcs and chords of a circle. Key Vocabulary: Circle Central Angle Radius Pythagorean Theorem Chords Right Triangle Major Arcs Minor Arcs

CHORDS AND ARCS An ARC is a part of a circle. Arc AB is an arc of ⊙O. A CENTRAL ANGLE of a circle is an angle whose vertex is the center of the circle. Minor Arc Major Arc Semicircle

CHORDS AND ARCS •

CHORDS AND ARCS Postulate 1: The measure of a central angle of a circle is equal to the measure of its intercepted arc. Example 1: Given: ⊙N with m ∠ONE=35 Find: Answer:

CHORDS AND ARCS Postulate 2: The measure of adjacent non-overlapping arcs is the sum of the measures of the two arcs. Sample Problem 1:

CHORDS AND ARCS Postulate 2: The measure of adjacent non-overlapping arcs is the sum of the measures of the two arcs. Sample Problem 1: Solution:

CHORDS AND ARCS Postulate 3: A diameter divides a circle into two semicircles. Sample Problem 2:

CHORDS AND ARCS Postulate 3: A diameter divides a circle into two semicircles. : Sample Problem 2: Solution: Since a central angle and its intercepted arc have equal measures Since arc (LE) is a semicircle. By the Arc Addition Postulate, we have Since a central angle and its intercepted arc have equal measures.

CHORDS AND ARCS CHORDS Theorem 1: If the diameter is perpendicular to a chord, then it bisects the chord and its minor and major arcs. Example 2:

CHORDS AND ARCS Theorem 2: If a diameter bisects a chord that is not a diameter, then it is perpendicular to the chord and bisects its major and minor arcs. Refer to the figure complete each statement. AD = _____ OE = _____

CHORDS AND ARCS Theorem 2: If a diameter bisects a chord that is not a diameter, then it is perpendicular to the chord and bisects its major and minor arcs. Refer to the figure complete each statement. AD = _____ OE = _____ Solution:

CHORDS AND ARCS Theorem 3: The perpendicular bisector of a chord contains the center of the circle. Theorem 4: In the same circle or in congruent circles congruent chords are equidistance from the center. Theorem 5: In the same circle or in the congruent circles, chords equidistance from the center is congruent.

CHORDS AND ARCS Sample Problem 4: Refer to the figure to complete each statement: AB = _______ x = ____ Solution: AB = 8 X=3