5.1 Arcs Intro

◡ Just as a SECTOR of a circle is part of the AREA....... An ARC of a circle is part of the CIRCUMFERENCE The ARC of a circle has the same angle measure as the central angle that forms it. 120 ∘ arc ? central angle ? MQ and NR are diameters. Find the indicated measure. (arc MN has the same measure as angle MON) N M 82 P O 63 Q arc MN = R ∘ MQ and NR are diameters. Find the indicated measure. (arc MN has the same measure as angle MON) N M 82 P O 63 Q arc MN = R Vertical Angles are ≅ 63 ∘ MQ and NR are diameters. Find the indicated measure. arc QR N M 82 P ∘ O 63 Q R MQ and NR are diameters. Find the indicated measure. N M 82 P O 63 Q arc PQ = R ∘ Every diameter has a central angle of 180. MQ and NR are diameters. Find the indicated measure. N ◡ M 82 P O 63 Q arc PQ = R Central angle 180 -82 -63 35 35 ∘ MQ and NR are diameters. Find the indicated measure. arc NQ N M 82 ∘ P O 63 Q R MQ and NR are diameters. Find the indicated measure. arc NQR N M 82 P ∘ O 63 Q R MQ and NR are diameters. Find the indicated measure. arc MR N M 82 P ∘ O 63 Q R MQ and NR are diameters. Find the indicated measure. arc PRN N M 82 P O 63 ∘ Q R 120 70 ∘ ∘ 120 ∘ 120 70 ∘ ∘ Congruent chords form congruent arcs Congruent chords form congruent arcs Find arc MN. M P N ∘ 68 Q ∘ Find arc MN. M P N ∘ 76 Q ∘ M 4x ∘ P N 80 Q Congruent chords form congruent arcs 4x = x = ∘ ∘ The arc MN is congruent to to which arc????? M 85 ∘ P N arc MP arc PQ arc QN arc MQ 65 ∘ Q M 85 ∘ P N 65 ∘ Q Arc MN is congruent to arc PQ. (≅ chords form ≅ arcs) If arc MN is represented by the variable x, what variable should be used to represent congruent (≅) arc PQ? Complete the equation with the total measure of every arc on the circle 85+65+x+x = M x 85 ∘ ∘ P N 65 x ∘ ∘ Q ∘ M x 85 ∘ ∘ P N 65 x ∘ ∘ ∘ Q 85+65+x+x = + = 360 360 M x 85 ∘ ∘ P N 65 x ∘ ∘ Q -150 150 85+65+x+x = + 2x 2x = x = = 360 360 -150 ∘ ∘ |

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