If g is a group, then a subgroup h is called characteristic if whenever ø : g -> g is an automorphism, ø(h) = h. prove that a characteristic subgroup is a normal subgroup. the opposite is not true in general. give an example of a group and a proper characteristic subgroup (hint: think about cyclic groups, or the center of a group)

Round 0.866 to the nearest hundredth

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In the following diagram it is given that dec,ab || dc, ad || eb, and ad is congruent to bc. a)why isn't abc a parallelogram even though it has a pair of parallel sides and a pair of congruent sides b)explain why be must be congruent to bc. further explain what type of triangle this makes triangle abc and what it tells you about angle 1 and angle 2c) finally why must angle 3 be congruent to angle 1? further, explain why we know that angle 3 is congruent to angle 2