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

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

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter4: Quadrilaterals

Section4.3: The Rectangle, Square, And Rhombus

Problem 42E: a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three...

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