Match the reasons with the statements in the proof to prove that triangle abc is congruent to triangle abd, given that ab ⊥ bd, ab ⊥ bc, and ac = ad. given: ab ⊥ bd ab ⊥ bc ac = ad prove: △abc ≅ △abd 1. ab ⊥ bd, ab ⊥ bc, ac = ad perpendicular lines form right angles 2. ∠abc and ∠abd are right angles reflexive property of equality 3. ab = ab hypotenuse - leg postulate 4. △abc ≅ △abd given

Which of the following represents a number squared is equal to twenty more than nine times that number ? a) x squared = 9x + 20 b) x squared = 20x + 9 c) x squared > 9 + 20x d) x squared = 9 + x + 20

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."

Ray ce is the angle bisector of zacd, which statement about the figure must be true? mzecd-mzecb mzace « 4mzacd zace - zdcb zecd zacd save and exit