Honors Geometry Formative Assessment: Sections * Required

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1 Honors Geometry Formative Assessment: Sections * Required 1. First Name * 2. Last Name * Page , 4, 16, 64, 256 * Make a conjecture about the next item in the sequence , 8, 32, 30, 120 * Make a conjecture about the next item in the sequence Given: points A, B, C, and D Conjecture: A, B, C, and D are coplanar. * False; the four points do not have to be in a straight line. False; two points are always coplanar but four are not. False; three points are always coplanar but four are not. 1/7

2 6. Given: Point B is in the interior of <ADC. Conjecture: <ADB = <BDC False; m<adb may be obtuse. False; just because it is in the interior does not mean it is on the bisecting line. False; m<adb + m<bdc = Given: points R, S, and T Conjecture: R, S, and T are coplanar. * False; the points do not have to be in a straight line. False; the points to not have to form right angles. False; one point may not be between the other two. 8. Given: Two angles are supplementary. Conjecture: They are both acute angles. * False; either both are right or they are adjacent. False; either both are right or one is obtuse. False; they must be vertical angles. Page 2 9. * An isosceles triangle has two congruent sides and a right angle measures 90 ; true. An isosceles triangle has two congruent sides or a right angle measures 90 ; true. An isosceles triangle has two congruent sides or four points are always coplanar; true. An isosceles triangle has two congruent sides or a right angle measures 90 ; false. 2/7

3 10. * false. false. true. true. A right angle measures 90 or four points are always coplanar, and a decagon has 12 sides; A right angle measures 90 and four points are always coplanar, or a decagon has 12 sides; A right angle measures 90 and four points are always coplanar, or a decagon has 12 sides; A right angle measures 90 or four points are always coplanar, and a decagon has 12 sides; 11. * Four points are always coplanar and a right angle measures 90 ; false. Four points are always coplanar and a right angle measures 90 ; true. Four points are always coplanar or a right angle measures 90 ; false. Four points are always coplanar or a right angle measures 90 ; true. Page 3 Forms of the Conditional 12. Determine the HYPOTHESIS and CONCLUSION: If the angles are vertical then they are congruent. * H: If the angles are vertical, C: then they are congruent H: If the angles are congruent, C: then they are vertical H: the angles are vertical, C: they are congruent H: they are congruent, C: The angles are vertical 13. A counterexample invalidates a statement. * Write the statement in if then form. If it invalidates the statement, then there is a counterexample. If there is a counterexample, then it invalidates the statement. If it is true, then there is a counterexample. If there is a counterexample, then it is true. 3/7

4 14. Two angles measuring 90 are complementary. * Write the statement in if then form. If two angles measure 90, then two angles measure 90. If two angles measure 90, then the angles are complementary. If the angles are supplementary, then two angles measure 90. If the angles are complementary, then the angles are complementary. 15. If you have a dog, then you are a pet owner. * Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample. If you are a pet owner, then you have a dog. A dog owner owns a pet. If you are a pet owner, then you have a dog. False; you could own a hamster. If you have a dog, then you are a pet owner. 16. All Jack Russells are terriers. * Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample. If a dog is a terrier, then it is a Jack Russell. False; it could be a Scottish terrier. If it is a Jack Russell, then a dog is a terrier. If a dog is a terrier, then a dog is a terrier. All Jack Russells are terriers. Page People who live in Texas live in the United States. Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample. People who do not live in the United States do not live in Texas. People who do not live in Texas do not live in the United States. False; they could live in Oklahoma. People who live in the United States live in Texas. False; they could live in Oklahoma. People who do not live in Texas live in the United States. 4/7

5 18. All quadrilaterals are four sided figures. * Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample. All non quadrilaterals are four sided figures. False; a triangle is a non quadrilateral. All four sided figures are quadrilaterals. No quadrilaterals are not four sided figures. No four sided figures are not quadrilaterals. 19. If you are 16 years old, then you are a teenager. * Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample. If you are not a teenager, then you are not 16 years old. If you are not 16 years old, then you are not a teenager. False; you could be 17 years old. If you are not a teenager, then you are 16 years old. If you are a teenager, then you are 16 years old. False; you could be 17 years old. 20. A converse statement is formed by exchanging the hypothesis and conclusion of the conditional. * Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample. A non converse statement is not formed by exchanging the hypothesis and conclusion of the conditional. A statement not formed by exchanging the hypothesis and conclusion of the conditional is a converse statement. False; an inverse statement is not formed by exchanging the hypothesis and conclusion of the conditional. A non converse statement is formed by exchanging the hypothesis and conclusion of the conditional. False; an inverse statement is formed by negating both the hypothesis and conclusion of the conditional. A statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement. Page (1) If I walk into a store, I buy a candy bar. (2) I have a candy bar. (3) I walked into a store. * Determine whether statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid. invalid yes; Law of Syllogism yes; Law of Detachment 5/7

6 22. (1) You are in ninth grade. (2) People who are in ninth grade floss their teeth regularly. (3) You floss your teeth regularly. * Determine whether statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid. yes; Law of Syllogism invalid yes; Law of Detachment Page 7 Determine if Inductive or was used to formulate the conclusion. 23. Amanda was learning to drive when her father told her to never run the car if the overheat light comes on. Last summer while driving to Evansville, her overheat light turned on so she turned off the car and called for help. * 24. Mia came to class late this morning. Mia s hair was uncombed. Mia is very fussy about her hair. Conclusion: Mia overslept. * 25. Tom knows that if he misses the practice the day before a game, then he will not be a starting player in the game. Tom misses practice on Tuesday. Conclusion: He will not be able to start in the game on Wednedsay. * 26. John always listens to his favorite radio station, an oldies station, when he drives his car. Every morning he listens to his radio on the way to work. On Monday, when he turns on his car radio, it is playing country music. Conclusion: Someone else has been driving his car. * 6/7

7 27. The Giants have lost their last seven games. Conclusion: The Giants will lose their next game. * 28. First Name 29. Last Name Powered by 7/7