11 2 Arcsand and Chords Up Lesson Presentation

11 -2 Arcsand and. Chords Up Lesson Presentation Lesson Quiz Holt Geometry

11 -2 Arcs and Chords Warm Up 1. What percent of 60 is 18? 30 2. What number is 44% of 6? 2. 64 3. Find m WVX. 104. 4 Holt Geometry

11 -2 Arcs and Chords Objectives Apply properties of arcs. Apply properties of chords. Holt Geometry

11 -2 Arcs and Chords Vocabulary central angle arc minor arc major arc Holt Geometry semicircle adjacent arcs congruent arcs

11 -2 Arcs and Chords A central angle is an angle whose vertex is the center of a circle. An arc is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them. Holt Geometry

11 -2 Arcs and Chords Holt Geometry

11 -2 Arcs and Chords Writing Math Minor arcs may be named by two points. Major arcs and semicircles must be named by three points. Holt Geometry

11 -2 Arcs and Chords Example 1: Data Application The circle graph shows the types of grass planted in the yards of one neighborhood. Find m. KLF = 360° – m KJF = 0. 35(360 ) = 126 m. KLF = 360° – 126° = 234 Holt Geometry

11 -2 Arcs and Chords Check It Out! Example 1 Use the graph to find each of the following. a. m FMC = 0. 30(360 ) = 108 Central is 30% of the . c. m EMD = 0. 10(360 ) b. m. AHB = 360° – m AMB m AHB = 360° – 0. 25(360 ) = 36 = 270 Holt Geometry Central is 10% of the .

11 -2 Arcs and Chords Adjacent arcs are arcs of the same circle that intersect at exactly one point. RS and ST are adjacent arcs. Holt Geometry

11 -2 Arcs and Chords Example 2: Using the Arc Addition Postulate Find m. BD. m. BC = 97. 4 Vert. s Thm. m CFD = 180 – (97. 4 + 52 ) = 30. 6 ∆ Sum Thm. m. CD = 30. 6 m. BD = m. BC + m. CD = 97. 4 + 30. 6 = 128 Holt Geometry m CFD = 30. 6 Arc Add. Post. Substitute. Simplify.

11 -2 Arcs and Chords Check It Out! Example 2 a Find each measure. m. JKL m KPL = 180° – (40 + 25)° m. KL = 115° m. JKL = m. JK + m. KL = 25° + 115° = 140° Holt Geometry Arc Add. Post. Substitute. Simplify.

11 -2 Arcs and Chords Check It Out! Example 2 b Find each measure. m. LJN = 360° – (40 + 25)° = 295° Holt Geometry

11 -2 Arcs and Chords Within a circle or congruent circles, congruent arcs are two arcs that have the same measure. In the figure ST UV. Holt Geometry

11 -2 Arcs and Chords Holt Geometry

11 -2 Arcs and Chords Example 3 A: Applying Congruent Angles, Arcs, and Chords TV WS. Find m. WS. TV WS m. TV = m. WS 9 n – 11 = 7 n + 11 2 n = 22 n = 11 chords have arcs. Def. of arcs Substitute the given measures. Subtract 7 n and add 11 to both sides. Divide both sides by 2. m. WS = 7(11) + 11 Substitute 11 for n. Simplify. = 88° Holt Geometry

11 -2 Arcs and Chords Example 3 B: Applying Congruent Angles, Arcs, and Chords C J, and m GCD m NJM. Find NM. GD NM GCD NJM GD NM arcs have chords. GD = NM Def. of chords Holt Geometry

11 -2 Arcs and Chords Example 3 B Continued C J, and m GCD m NJM. Find NM. 14 t – 26 = 5 t + 1 9 t = 27 t=3 NM = 5(3) + 1 = 16 Holt Geometry Substitute the given measures. Subtract 5 t and add 26 to both sides. Divide both sides by 9. Substitute 3 for t. Simplify.

11 -2 Arcs and Chords Check It Out! Example 3 a PT bisects RPS. Find RT. RPT SPT m. RT m. TS RT = TS 6 x = 20 – 4 x 10 x = 20 x=2 RT = 6(2) RT = 12 Holt Geometry Add 4 x to both sides. Divide both sides by 10. Substitute 2 for x. Simplify.

11 -2 Arcs and Chords Check It Out! Example 3 b Find each measure. A B, and CD EF. Find m. CD. chords have arcs. m. CD = m. EF 25 y = (30 y – 20) Substitute. Subtract 25 y from both sides. Add 20 20 = 5 y to both sides. Divide both sides by 5. 4=y Substitute 4 for y. CD = 25(4) m. CD = 100 Holt Geometry Simplify.

11 -2 Arcs and Chords Holt Geometry

11 -2 Arcs and Chords Example 4: Using Radii and Chords Find NP. Step 1 Draw radius RN. RN = 17 Radii of a are . Step 2 Use the Pythagorean Theorem. SN 2 + RS 2 = RN 2 SN 2 + 82 = 172 SN 2 = 225 SN = 15 Substitute 8 for RS and 17 for RN. Subtract 82 from both sides. Take the square root of both sides. Step 3 Find NP. NP = 2(15) = 30 Holt Geometry RM NP , so RM bisects NP.

11 -2 Arcs and Chords Check It Out! Example 4 Find QR to the nearest tenth. Step 1 Draw radius PQ. PQ = 20 Radii of a are . Step 2 Use the Pythagorean Theorem. TQ 2 + PT 2 = PQ 2 Substitute 10 for PT and 20 for PQ. TQ 2 + 102 = 202 Subtract 102 from both sides. TQ 2 = 300 Take the square root of both sides. TQ 17. 3 Step 3 Find QR. QR = 2(17. 3) = 34. 6 Holt Geometry PS QR , so PS bisects QR.

11 -2 Arcs and Chords Lesson Quiz: Part I 1. The circle graph shows the types of cuisine available in a city. Find m. TRQ. 158. 4 Holt Geometry

11 -2 Arcs and Chords Lesson Quiz: Part II Find each measure. 2. NGH 3. HL Holt Geometry 139 21

11 -2 Arcs and Chords Lesson Quiz: Part III 4. T U, and AC = 47. 2. Find PL to the nearest tenth. 12. 9 Holt Geometry