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5-Minute Check on Lesson 10-2

Transparency 10-3. 5-Minute Check on Lesson 10-2. In ⊙ O, BD is a diameter and m AOD =55 °. Find each measure. m COB m DOC m AOB Refer to ⊙ P. Find each measure. 4. mLM 5. mMOL .

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5-Minute Check on Lesson 10-2

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  1. Transparency 10-3 5-Minute Check on Lesson 10-2 • In ⊙O, BD is a diameter and mAOD =55°. Find each measure. • mCOB • mDOC • mAOB • Refer to ⊙P. Find each measure. • 4. mLM • 5. mMOL • The radius of ⊙R is 35, LM NO, LM = 45 and mLM = 80.Find each measure. • m NO • m NQ • NO • NT • RT • Which congruence statement is true if RS and TU are congruent chords of ⊙V? 114° 80° 66° 40° 125° 45 22.5 26.81 150° Standardized Test Practice: 210° RS  ST RS  SU RS  TU ST  RU A B C D B Click the mouse button or press the Space Bar to display the answers.

  2. Lesson 10-4 Inscribed Angles

  3. Objectives • Find measures of inscribed angles • Find measures of angles of inscribed polygons

  4. Vocabulary • Inscribed Angle – an angle with its vertex on the circle and chords as its sides

  5. y x Circles – Inscribed Angles J Y° Center F X° Inscribe Angles -- Measure Y° = ½ X°(central angle) E K Measure Y° = ½ measure Arc KEF

  6. In and Find the measures of the numbered angles. First determine Example 4-1a Arc Addition Theorem

  7. So, m Example 4-1b Simplify. Subtract 168 from each side. Divide each side by 2.

  8. Answer: Example 4-1d

  9. In and Find the measures of the numbered angles. Answer: EXAMPLE 2 Example 4-1e

  10. ALGEBRATriangles TVU and TSU are inscribed in with Find the measure of each numbered angle if and EXAMPLE 3 Example 4-4a ∆UVT and ∆ UST are right triangles. Since they intercept congruent arcs, then m1 = m2. The third angles of the triangles must also be congruent, so m2 = m4 .

  11. Use the value of x to find the measures of Answer: EXAMPLE 3 (CONT) Example 4-4b Angle Sum Theorem Simplify. Subtract 105 from each side. Divide each side by 3. Given Given

  12. ALGEBRATriangles MNO and MPO are inscribed in with Find the measure of each numbered angle if and Answer: Example 4-4d EXAMPLE 4

  13. Quadrilateral QRST is inscribed in If and Find and Example 4-5a Draw a sketch of this situation.

  14. To find we need to know To find first find Example 4-5b Inscribed Angle Theorem Sum of angles in circle=360 Subtract 174 from each side. Inscribed Angle Theorem Substitution Divide each side by 2.

  15. To find we need to know but first we must find Answer: Example 4-5c Inscribed Angle Theorem Sum of angles in circle=360 Subtract 204 from each side. Inscribed Angle Theorem Divide each side by 2.

  16. Quadrilateral BCDE is inscribed in If and find and Answer: Example 4-5e EXAMPLE 6

  17. Summary & Homework • Summary: • The measure of the inscribed angle is half the measure of its intercepted arc • The angles of inscribed polygons can be found by using arc measures • Homework: • pg 549-550; (8-10, 13-15, 22-25)

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