Houghton Mifflin Harcourt Publishing Company 3 PROOF Inscribed Quadrilateral Theorem Given: Quadrilateral ABCD is inscribed in circle O. Prove: LA and LC are supplementary; LB and D are supplementary. ABCD and DAB make a complete circle. Therefore, B mBCD + mDAB = 360° ZA is an inscribed angle and its intercepted arc is BCD; LC is an inscribed angle and its intercepted arc is DAB. By the Inscribed Angle Theorem, mZA= and m/C= C So, mZA+mZC=. Substitution Distributive Property Substitution Simplify. This shows that LA and ZC are supplementary. Similar reasoning shows that LB and 2D are supplementary. B

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