Consider an overlapping set of four circles A, B, C, D. One would like to position the circles so that every possible subset of the circles forms a region, e. g., four regions each contained in just one (different) circle, six regions formed by the intersection of two circles (AB, AC, AD, BC, BD, CD), four regions formed by the intersection of three of the four circles, and one region formed by the intersection of all four circles. Prove that it is not possible to have such a set of 15 bounded regions.

Select the correct answer. given: ∆abc with prove: statement reason 1. given 2. ∠cab ≅ ∠edb ∠acb ≅ ∠deb if two parallel lines are cut by a transversal, the corresponding angles are congruent. 3. ∆abc ~ ∆dbe aa criterion for similarity 4. corresponding sides of similar triangles are proportional. 5. ab = ad + db cb = ce + eb segment addition 6. substitution property of equality 7. division 8. subtraction property of equality what is the missing statement in the proof? scroll down to see the entire proof.