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GEOMETRY CHAPT. 2 PRACTICE TEST Determine if each conjecture is true or false. Explain your answer and give a counter example for each false conjecture. 1) Given: AB + BC = AC Conjecture: AB = BC Write each statement in if-then form. Identify the hypothesis and conclusion. The write the converse, inverse and contrapositive of the original if-then statement. 2) An acute angles has a measure less than 90 degrees Conditional = Hypothesis = Conclusion = Converse = Inverse = Contrapositive = Determine if a valid conclusion can be reached from the two true statements using the Law of Detachment or the Law of Syllogism. If a valid conclusion is possible, state it and the law that it used. If a valid conclusion does not follow, write no conclusion. 4) a) b) If two angles are complementary, then their sum is 90 degrees If the sum of both angles is 90 degrees, then both angles are acute 5) a) b) If two angles are vertical, then they are congruent. ∠1 and ∠2 are congruent. Name the property that justifies each statement. 6) If m∠1 = m∠2 then m∠2 = m∠1 7) If m∠1 = 90 and m∠1 = m∠2 , then m∠2 = 90 8) If AB = CD then 1 1 AB = CD 2 2 Determine whether the following statements are always, sometimes, or never true for problems 9 - 11. Justify all answers!!! 9) There is exactly one plane that contains three points. 10) Two lines can intersect at two points. 11) If two points lie in one plane than all points on that line would lie within the same plane. For each problem below, solve for x and each numbered angle. 12) 13) Complete the proofs below on a separate sheet of paper. Show all steps. 14) 15)