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Bailey Milani Geometry 2.2a Homework 1. Vocabulary: Copy and complete: The converse of a conditional statement is found by switching the hypothesis and the conclusion. 2. Writing: Write a definition for the term collinear points, and show how the definition can be interpreted as a biconditional. Definition: If two or more points lie on the same line, then they are collinear points. Biconditional: Two or more points are collinear points if and only if they lie on the same line. Rewriting Statements: Rewrite the conditional statement in if-­‐then form. 4. The measure of a straight angle is 180*. If the angle is 180*, then it is a straight angle. 5. Only people who are registered are allowed to vote. If a person is registered to vote, then they are allowed to vote. 6. Error Analysis: Describe and correct the error in writing the if-­‐then statement. Given statement: All High school students take four English courses. If-­‐then statement: If a high school student takes four courses, then all four are English courses. It doesn’t follow the given statement. If-­‐then statement: If you are a high school student, then you take four English courses. Writing Related Statements: For the given statement, write the if-­‐then form, the converse, the inverse, and the contrapositive. 7. The complementary angles add to 90*. If-­‐then form: If two angles are complementary, then they add to 90*. Converse: If two angles add to 90*, then they are complementary. Inverse: If two angles are not complementary, then they do not add to 90*. Contrapositive: If two angles do not add to 90*, then they are not complementary. 8. Ants are insects. If-­‐then form: If ants are insects, then they are insects. Converse: If insects are ants, then ants are insects. Inverse: If ants are not insects, then they are not insects. Contrapositive: If insects are not ants, then ants are not insects. 9. 3x + 10 = 16, because x = 2. If-­‐then form: If x = 2, then 3x + 10 = 16. Converse: If 3x + 10 = 16, then x = 2. Inverse: If x dose not = 2, then 3x + 10 dose not = 16. Contrapositive: If 3x + 10 dose not = 16, then x dose not = 2. 10. A midpoint bisects a segment. If-­‐then form: If a midpoint is in the middle, then it bisects a segment. Converse: If it bisects a segment, then it is the midpoint. Inverse: If a midpoint is not the middle, then it dose not bisect a segment. Contrapositive: If it dose not bisect the segment, then it is not the midpoint. Analyzing Statements: Decide whether the statement is true or false. If false, provide a counterexample. 13. Supplementary angles are always linear pairs. False, m<ABC = 30*, and m<DEF = 150*. 14. If a number is an integer, then it is rational. True 15. If a number is a real number, then it is irrational. False, 2 Algebra: Write the converse of each true statement. Tell whether the converse is true. If false, explain why. 26. If x > 4, then x > 0. Converse: If x > 0, then x > 4. False, 2 > 0, but not 4. 27. If x < 6, then –x > -­‐6. Converse: If –x > -­‐6, then x < 6. True 28. If x _< (less then or equal to) –x, then x _< 0. Converse: If x _< 0, then x _< -­‐x. True 29. Open-­‐Ended Math: Write a statement that is true but whose converse is false. If you can jump, then you will fall. Converse: If you can fall, then you will jump. Volcanoes: Solid fragments are sometimes ejected from volcanoes during an eruption. The fragments are classified by size. 31. A fragment is called a block or bomb if and only if its diameter is greater then 66 millimeters. True 32. A fragment is called a lapilli if and only if its diameter is less than 64 millimeters. False, It also, has to be greater than 2.