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# 9 5 Inscribed Angles

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### 9 5 Inscribed Angles

1. 1. 9-5 Inscribed Angles
2. 2. <ul><li>Inscribed angle – An angle where the vertex is on the circle and its arms are chords in the circle. </li></ul>Inscribed angle
3. 3. <ul><li>Intercepted arc – the part of the circle inside the arms of the angle </li></ul>Intercepted arc
4. 4. Lets go to the internet… Circle Fun
5. 5. <ul><li>Theorem – An inscribed angle is half of the intercepted arc. </li></ul>
6. 6. What is the measure of x? <ul><li>50° </li></ul><ul><li>60 </li></ul><ul><li>40° </li></ul><ul><li>20° </li></ul><ul><li>10° </li></ul>10 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
7. 7. What is the measure of y? <ul><li>50° </li></ul><ul><li>60° </li></ul><ul><li>40° </li></ul><ul><li>20° </li></ul><ul><li>10° </li></ul>10 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
8. 8. <ul><li>Corollary 1 – If two inscribed angles intercept the same arc, then the angles are congruent. </li></ul>1 2
9. 9. Lets go to the internet… Circle Fun
10. 10. <ul><li>Corollary 2 – An angle inscribed in a semicircle is a right angle. </li></ul>
11. 11. <ul><li>Corollary 3 – If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. </li></ul>F E D G m  D + m  F = 180 ° m  E + m  G = 180 °
12. 12. What is x? <ul><li>30° </li></ul><ul><li>40° </li></ul><ul><li>70° </li></ul><ul><li>90° </li></ul><ul><li>110° </li></ul><ul><li>140° </li></ul><ul><li>150° </li></ul>10 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
13. 13. What is y? <ul><li>30° </li></ul><ul><li>40° </li></ul><ul><li>70° </li></ul><ul><li>90° </li></ul><ul><li>110° </li></ul><ul><li>140° </li></ul><ul><li>150° </li></ul>10 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
14. 14. What is z? <ul><li>30° </li></ul><ul><li>40° </li></ul><ul><li>70° </li></ul><ul><li>90° </li></ul><ul><li>110° </li></ul><ul><li>140° </li></ul><ul><li>150° </li></ul>10 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
15. 15. Lets go to the internet… Circle Fun
16. 16. <ul><li>Theorem – The measure of an  formed by a chord and a tangent is equal to ½ the intercepted arc. </li></ul>1
17. 17. SPICSA <ul><li>Page 354 2-10 even </li></ul>