given: ∠1 ≅ ∠2

prove: a ∥ b

what is the missing statement in the proof?

∠1 ≅ ∠4

a ∥ b

∠1 ≅ ∠2

a ⊥ b

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

What is the order of these fractions from least to greatest 2/3 7/10 5/8 65/100

Solve each quadratic equation by factoring and using the zero product property. x^2 - 8x + 30 = 3x