1. Inscribed Angles LESSON 10–4

2. Lesson Menu Five-Minute Check (over Lesson 10–3) TEKS 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

3. Over Lesson 10–3 5-Minute Check 1 A.60 B.70 C.80 D.90

4. Over Lesson 10–3 5-Minute Check 2 A.40 B.45 C.50 D.55

5. Over Lesson 10–3 5-Minute Check 3 A.40 B.45 C.50 D.55

6. Over Lesson 10–3 5-Minute Check 4 A.40 B.30 C.25 D.22.5

7. Over Lesson 10–3 5-Minute Check 5 A.24.6 B.26.8 C.28.4 D.30.2

8. Over Lesson 10–3 5-Minute Check 6 A. B. C. D.

9. TEKS Targeted TEKS G.12(A) Apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems. Mathematical Processes G.1(F), G.1(G)

10. Then/Now You found measures of interior angles of polygons. Find measures of inscribed angles. Find measures of angles of inscribed polygons.

11. Vocabulary inscribed angle intercepted arc

12. Concept

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

14. Example 1 Use Inscribed Angles to Find Measures B. = 2(52) or 104

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

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

17. Concept

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

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

20. Concept

21. Example 4 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= 180 Angle Sum Theorem (x + 4) + (8x – 4) + 90 = 180Substitution 9x + 90= 180Simplify. 9x= 90Subtract 90 from each side. x= 10Divide each side by 9. Answer: So, m  B = 8(10) – 4 or 76.

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

23. Concept

24. Example 5 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.

25. Example 5 Find Angle Measures Since TSUV is inscribed in a circle, opposite angles are supplementary. m  S + m  V = 180 m  U + m  T = 180 m  S + 90 = 180(14x) + (8x + 4)= 180 m  S = 9022x + 4= 180 22x= 176 x= 8 Answer: So, m  S = 90 and m  T = 8(8) + 4 or 68.

26. Example 5 A.48 B.36 C.32 D.28 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.

27. Inscribed Angles LESSON 10–4