Choose from the following reasons below to prove the theorem. Some of them can be used twice. Factoring Addition property of equality Given The arc of the whole circle is 360º Inscribed angle theorem Definition of supplementary angles Substitution (steps 5 and 5) Algebraic process (step 6) Theorem: "If a quadrilateral in inscribed in a circle, then its opposite angles are supplementary." Given: Quadrilateral ABCD is inscribed in OE. Prove: ZADC and LABC are supplementary ZDAB and ZDCB are supplementary STATEMENT REASON 1. Quadrilateral ABCD is inscribed in OE. (1) 2. MLADC = =MABC (2) 1 MLABC =mĀDC 1 M2DAB = MDCB 1 MLDCB =MDAB Addition property of equality 3. MLADC + MLABC = MĀBC + MADC

oom.google.com/u/2/c/NDU4Njl1Mzk2MDI Open with - Pear Deck Interactive Slide Students, draw anywhere on this slide! Do no remove D 7. Isosceles triangle ABC is shown below with legs that measure 8 inches and a vertex angle of 50, (a) Determine the area of AABC. Note that you will need to use right triangle trigonometry. Round to the nearest tenth of a square inch. 8 in 50 (b) Determine the area of the circular sector. Again, round to the nearest tenth of a 8 in square inch. (c) Using your answers from (a) and (b), determine the area of the shaded region. Page 10 I 10 Q + 56°F ch 25 hp f6 fio & 6 8.