Conjectures are statements which are E believed to be true based on the current data or evidence. However, they have not yet been proven or disproven. To move toward logical proof, true statements that properly build on one another, along with justifications for those statements, are needed. Based on the diagram in Figure 1, provide a justification for F Figurel each statement. 1. :AGB, 40013, 4001), and :AGD are right angles. 2. E g BG g E g DG 3. AABG E ACBG g AADG E ACDG 4. E g 30 2 E g m 5. Sometimes when creating a proof, it is useful to add additional segments to a diagram. Amelia is conjecturing E 2 FD. To prove this conjecture, Amelia thinks she will need to add to the diagram in Figure 1. What would you add to the diagram? How might this addition of an auxiliary segment be used in the proof? E Figure 1