Honors Geometry Name___________________ Chp.1 and 2 Quiz 2nd/7th period, 9/10/07 A.M.D.G. 1) What is a plane? Explain so that a 10-year-old could understand. (5 points) A plane is a flat two-dimensional surface that extends forever in those two dimensions. 2) Can you ever bisect a line segment? Why or why not? (5 points) Yes, since a segment has a finite length, you can cut it into two equal lengths. 3) Find the midpoint of the line segment whose endpoints are (-12, 5) and (17, 12). Explain how you could demonstrate that the point you found is actually the midpoint. You do not actually have to prove this is the midpoint, but if you want to as part of your explanation, you may. (10 points) ⎛⎞x1212++xy y ⎜⎟, ⎝⎠22 ⎛⎞−+12 17 5 + 12 ⎜⎟, ⎝⎠22 ⎛⎞517 ⎜⎟, ⎝⎠22 You could graph the segment and measure it to confirm that you have a midpoint. 4) Explain what is wrong with the statement, AB= CD . What could you do to correct the statement? (5 points) The symbols, AB and CD , are indicating segments, so we should use AB≅ CD to indicate that the segments are congruent to each other. OR We could also say that AB= CD , indicating that the lengths are the same. 5) Write the converse and inverse of the following statement and indicate if each one is true or false: (10 points) If you bisect an obtuse angle, then the new angles are acute. Converse: If the new angles are acute, then you bisected an obtuse angle. False – you could bisect an acute angle and get two acute angles. Inverse: If you do not bisect an obtuse angle, then the new angles are not acute. False – you could get acute angles from cutting an obtuse angle into two non-congruent pieces. 6) Write a reason for each step in solving the algebra problem, 51253x +=() −x . (5 points) 51253x +=( −x) Given 512155x +=−x Distributive Property 10x += 12 15 Addition Prop. Of = 10x = 3 Addition Prop. Of = 3 x = Multiplication Prop. Of = 10 7) Assume all of the following statements are true, and use the information to respond to all of the following: (20 points total) If his friends come over, then Mr. Maychrowitz plays Tekken 5 with them. If Mr. Maychrowitz plays Tekken 5, then he plays Paul Phoenix. If Mr. M. plays Paul Phoenix, then he wins at Tekken 5. If Mr. M wins at Tekken 5, then he gloats. a) What can you conclude if Mr. M does not gloat? List any and all conclusions. b) What can you conclude if Mr. M plays Tekken 5? List any and all conclusions. c) What can you conclude if Mr. M’s friends don’t come over? List any and all conclusions. d) What can you conclude if Mr. M does not play Paul Phoenix? List any and all conclusions. a) He doesn’t win, doesn’t play Paul Phoenix, doesn’t play Tekken 5, and his friends don’t come over. b) He plays Paul Phoenix, wins at Tekken 5, and he gloats. c) You can’t conclude anything. d) He doesn’t play Tekken 5, and his friends did not come over. 8) Complete the following proof without using the Congruent Complements Theorem (assume that you have not proved that theorem yet) (20 points) Given: ∠∠1 and 2 are complementary ∠∠3 and 4 are complementary ∠≅∠14 ∠1 ∠2 ∠3 ∠4 Prove: ∠≅23∠ Statement Reason ∠1 and ∠2 are complementary Given ∠3 and ∠4 are complementary mm∠+12∠ =90D Definition of complementary angles D mm∠+34∠=90 mm∠+12∠ =m∠3+m∠4 Transitive Property of Equality ∠≅14∠ Given mm∠=14∠ Definition of Congruence mm∠+12∠ =m∠3+m∠1 Substitution Property of Equality mm∠=23∠ Addition Property of Equality ∠≅23∠ Definition of Congruence .