10.3 Arcs and Chords Learning Objectives: Recognize and use relationships between arcs and chords Recognize and use relationships between arcs, chords, and diameters

Vocab Chord

Example 1 A circular piece of jade is hung from a chain by two wires around the stone. 𝐽𝑀 ≅ 𝐾𝐿 and 𝑚 𝐾𝐿 =90°. Find the 𝑚 𝐽𝑀 . ʘW has congruent chords 𝑅𝑆 & 𝑇𝑉 . If 𝑚 𝑅𝑆 =85°, find 𝑚 𝑇𝑉 . 𝑚 𝐾𝐿 =𝑚 𝐽𝑀 𝑚 𝐽𝑀 =90° 𝑚 𝑅𝑆 =𝑚 𝑇𝑉 𝑚 𝐽𝑀 =85°

Example 2 In the figure ʘA ≅ ʘB and 𝑊𝑋 ≅ 𝑌𝑍 . Find WX. In the figure ʘG ≅ ʘH and 𝑅𝑇 ≅ 𝐿𝑀 . Find LM 7𝑥−2=5𝑥+6 2𝑥=8 𝑥=4 𝑊𝑋=7 4 −2=24 3𝑥−5=2𝑥+1 𝑥=6 𝐿𝑀=2 6 +1=13

Vocab Theorem 10.3 Theorem 10.4

Example 3 a) b) In ʘG, 𝑚 𝐷𝐸𝐹 =150°. Find 𝑚 𝐷𝐸 In ʘZ, 𝑚 𝑊𝑈𝑋 =60°. Find 𝑚 𝑈𝑋 . 𝑚 𝐷𝐸 =𝑚 𝐸𝐹 𝑚 𝐷𝐸 = 150 2 =75° 𝑚 𝑈𝑊 =𝑚 𝑈𝑋 𝑚 𝐷𝐸 = 60 2 =30°

Example 4 In the ceramic stepping stone below, diameter 𝐴𝐵 is 18 inches long and chord 𝐸𝐹 is 8 inches long. Find CD. In the circle below, diameter 𝑄𝑆 is 14 inches long and chord 𝑅𝑇 is 10 inches long. Find VU. Since 𝐴𝐵 is the diameter, the radius is 9 in. You can create another radius from point C to E and use the Pythagorean theorem to solve. 𝑥 2 + 4 2 = 9 2 𝑥 2 +16=81 𝑥 2 =65 𝑥= 65 9 in 4 in x 𝑥 2 + 5 2 = 7 2 𝑥 2 +25=49 𝑥 2 =24 𝑥=2 6 7 in 5 in x

Vocab Theorem 10.5

Example 5 a) b) In ʘP EF = GH = 24. Find PQ. In ʘR MN = PO = 29. Find RS. 4𝑥−3=2𝑥+3 𝑥=3 𝑃𝑄=4 3 −3=9 3𝑥−6=𝑥+8 𝑥=7 𝑅𝑆=7+8=15

Summary 1. Find the value of x. 2. Find the value of x.