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Splash Screen. Five-Minute Check (over Lesson 10–3) NGSSS Then/Now New Vocabulary Theorem 10.6: Inscribed Angle Theorem Proof: Inscribed Angle Theorem (Case 1) Example 1: Use Inscribed Angles to Find Measures Theorem 10.7 Example 2: Use Inscribed Angles to Find Measures

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 10–3) NGSSS Then/Now New Vocabulary Theorem 10.6: Inscribed Angle Theorem Proof: Inscribed Angle Theorem (Case 1) Example 1: Use Inscribed Angles to Find Measures Theorem 10.7 Example 2: Use Inscribed Angles to Find Measures Example 3: Use Inscribed Angles in Proofs Theorem 10.8 Example 4: Find Angle Measures in Inscribed Triangles Theorem 10.9 Example 5: Real-World Example: Find Angle Measures Lesson Menu

  3. A B C D A. 60 B. 70 C. 80 D. 90 5-Minute Check 1

  4. A B C D A. 40 B. 45 C. 50 D. 55 5-Minute Check 2

  5. A B C D A. 40 B. 45 C. 50 D. 55 5-Minute Check 3

  6. A B C D A. 40 B. 30 C. 25 D. 22.5 5-Minute Check 4

  7. A B C D A. 24.6 B. 26.8 C. 28.4 D. 30.2 5-Minute Check 5

  8. A B C D A. B. C. D. 5-Minute Check 6

  9. MA.912.G.6.1Determine the center of a given circle. Given three points not on a line, construct the circle that passes through them. Construct tangents to circles. Circumscribe and inscribe circles about and within triangles and regular polygons. MA.912.G.6.4 Determine and use measures of arcs and related angles. Also addresses MA.912.G.6.3. NGSSS

  10. You found measures of interior angles of polygons. (Lesson 6–1) • Find measures of inscribed angles. • Find measures of angles of inscribed polygons. Then/Now

  11. inscribed angle • intercepted arc Vocabulary

  12. Concept

  13. Concept

  14. Use Inscribed Angles to Find Measures A. Find mX. Answer:mX = 43 Example 1

  15. B. Use Inscribed Angles to Find Measures = 2(252) or 104 Example 1

  16. A B C D A. Find mC. A. 47 B. 54 C. 94 D. 188 Example 1

  17. A B C D B. A. 47 B. 64 C. 94 D. 96 Example 1

  18. Concept

  19. RS R and S both intercept . Use Inscribed Angles to Find Measures ALGEBRA Find mR. mRmS Definition of congruent angles 12x – 13 = 9x + 2 Substitution x = 5 Simplify. Answer:So, mR = 12(5) – 13 or 47. Example 2

  20. A B C D ALGEBRA Find mI. A. 4 B. 25 C. 41 D. 49 Example 2

  21. Write a two-column proof. Given: Prove: ΔMNP ΔLOP Proof: Statements Reasons LO  MN2. If minor arcs are congruent, then corresponding chords are congruent. Use Inscribed Angles in Proofs 1.Given Example 3

  22. Proof: Statements Reasons M intercepts and L intercepts . 3. Definition of intercepted arc Use Inscribed Angles in Proofs M  L4. Inscribed angles of the same arc are congruent. MPN  OPL 5. Vertical angles are congruent. ΔMNP  ΔLOP 6. AAS Congruence Theorem Example 3

  23. Write a two-column proof. Given: Prove: ΔABE ΔDCE Select the appropriate reason that goes in the blank to complete the proof below. Proof: Statements Reasons AB  DC2. If minor arcs are congruent, then corresponding chords are congruent. 1.Given Example 3

  24. Proof: Statements Reasons D intercepts and A intercepts . 3. Definition of intercepted arc D  A4. Inscribed angles of the same arc are congruent. DEC  BEA 5. Vertical angles are congruent. ΔDCE  ΔABE 6. ____________________ Example 3

  25. A B C D A. SSS Congruence Theorem B. AAS Congruence Theorem C. Definition of congruent triangles D. Definition of congruent arcs Example 3

  26. Concept

  27. Find Angle Measures in Inscribed Triangles ALGEBRA Find mB. ΔABC is a right triangle because C inscribes a semicircle. mA + mB + mC = 180Angle Sum Theorem (x + 4) + (8x – 4) + 90 = 180 Substitution 9x + 90 = 180 Simplify. 9x = 90 Subtract 90 from each side. x = 10 Divide each side by 9. Answer:So, mB = 8(10) – 4 or 76. Example 4

  28. A B C D ALGEBRA Find mD. A. 8 B. 16 C. 22 D. 28 Example 4

  29. Concept

  30. Find Angle Measures INSIGNIAS An insignia is an emblem that signifies rank, achievement, membership, and so on. The insignia shown is a quadrilateral inscribed in a circle. Find mS and mT. Example 5

  31. Find Angle Measures Since TSUV is inscribed in a circle, opposite angles are supplementary. S + V = 180S + V = 180 S + 90= 180 (14x) + (8x + 4) = 180 S = 90 22x + 4 = 180 22x = 176 x = 8 Answer:So, mS = 90 and mT = 8(8) + 4 or 68. Example 5

  32. A B C D INSIGNIAS An insignia is an emblem that signifies rank, achievement, membership, and so on. The insignia shown is a quadrilateral inscribed in a circle. Find mN. A. 48 B. 36 C. 32 D. 28 Example 5

  33. End of the Lesson

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