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Understanding Inscribed Angles and Polygons in Circles

This lesson focuses on the properties of inscribed angles and polygons within a circle. Students will learn that inscribed angles are half the measure of the intercepted arc. They will also explore congruency in inscribed angles that intercept the same arc, and the significance of right angles in inscribed angles leading to semicircles. Additionally, the lesson covers quadrilaterals inscribed in circles, revealing that opposite angles are supplementary. Through various practice problems, students will apply these principles to solve for angle measures and arc lengths.

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Understanding Inscribed Angles and Polygons in Circles

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Presentation Transcript

  1. 10-4 Inscribed AnglesN# 4 4/9/2014 SLG : Students will be able to find measures of inscribed angles and inscribed polygons.

  2. D Inscribed angles are equal to half of the arc they intercept. C B E B If two inscribed angles of a circle intercept the same arc, then they are congruent. D C E If an inscribed angle equals 90 degrees, then the arc that it intercepts will be a semicircle, and its endpoints are the endpoints of the diameter. D B D C E B D If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. C F

  3. A A E1 E2 B 59 B D 36 D 40 C 94 C m arc AC = ______ m < BCD = ______ m < BDC = ______ m arc AD = ______ A E4 A E3 B 2x+15 12x-13 3x-5 B D D C C 9x+2 m < ADB = ______ m < ACB = ______ m < CBD = ______ m arc CD = ______

  4. 4x+2 E5 A E6 A 8x-4 x+4 C 9x-3 B C B m < A = ______ m < C = ______ m < A = ______ m < C = ______ A E8 A E7 B 14x 95 90 B 60 D 8x+4 D C C m < D = ______ m < C = ______ m < A = ______ m < D = ______

  5. A# 9 4/9/2014 PWS 10-4

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