5-Minute Check on Lesson 10-3 Transparency 10-4 Click the mouse button or press the Space Bar to display the answers. The radius of ⊙ R is 35, LM  NO, LM = 45 and mLM = 80. Find each measure. 1.m NO 2.m NQ 3.NO 4.NT 5.RT 6. Which congruence statement is true if RS and TU are congruent chords of ⊙ V? Standardized Test Practice: ACBD RS  SURS  TUST  RU RS  ST 45 80° 40° B

Lesson 10-4 Inscribed Angles

Objectives Find measures of inscribed angles Find measures of angles of inscribed polygons

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

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

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

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

Example 4-1d Answer:

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

Example 4-4a ALGEBRA Triangles TVU and TSU are inscribed in with Find the measure of each numbered angle if and ∆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.

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

Example 4-4d Answer: ALGEBRA Triangles MNO and MPO are inscribed in with Find the measure of each numbered angle if and

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

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

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

Example 4-5e Answer: Quadrilateral BCDE is inscribed in If and find and

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 ; 7, 9,10, 15, 22-25