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Geometry Assignment 5E Name _____________________________ Period ________ Date ________________ For questions 1-9, decide which congruence postulate, if any, you can use to prove that the given triangles are congruent. Write the congruence statement and identify the postulate. 1. B 6. F Q Y C D P G E Z R 2. X G H E F 7. B 3. A D C D F E C B E 8. C 4. R 3" T C 2" 2" S 3" B D E A A F B 9. 5. R M L N Created 6/2010 Q S Printed 4/28/2017 Geometry Assignment 5E 10. Name _____________________________ Period ________ Date ________________ Given the diagram below. 12. Given the diagram below. F Z I X Y V J W H G If VY XY , which congruence postulate/theorem justifies VYZ XYE ? Which corresponding parts need to be congruent in order to prove FJH GJI by SSS? a. b. c. d. 11. HJF IJG FJ GJ FH GI FHJ GIJ Given the diagram below. A E F a. SSS b. SAS c. ASA d. AAS e. HL For #13-15, the proof is in the incorrect order. Write a correct order of the steps for each proof. 13. Given: FH bisects GFJ and GHJ C B D Prove: GFH JFH G If BC EF , which congruence postulate/theorem justifies that ABC DEF ? a. b. c. d. e. HL SAS SSS AAS ASA Created 6/2010 F 2 1 3 4 H J Statement 1. 2 1 3 4 Reason 1. Definition of angle bisector 2. GFH JFH 2. ASA 3. FH bisects GFJ and GHJ 3. Given 4. FH FH 4. Reflexive property Printed 4/28/2017 Geometry Assignment 5E 14. Name _____________________________ Period ________ Date ________________ Given: AB AD and DE AD BC EC For # 16-18, one of the reasons is incorrect. Which reason is wrong? Write the correct reason. Prove: ABC DEC 16. Given: AB DE , BC EF , E AC DF Prove: ABC DEC A C A D D B B Statement 1. ACB DCE Reason 1. Vertical Angles Theorem 2. A D 2. all right angles are congruent (Euclid) 3. AB AD DE AD BC EC 4. ABC DEC 5. A and D are right angles 15. C F E Statement 1. AB DE 2. BC EF Reason 1. Given 2. Given 3. AC DF 3. Reflexive Property 4. ABC DEF 4. SSS 3. Given 4. AAS 17. 5. Definition of perpendicular Given: MH MK ; HJ KJ MJH and MJK are right angles Given: PN bisects MNO , MN NO Prove: MNP ONP N M M Prove: H K H J K O P Statement 1. PN bisects MNO ; MN NO Reason 1. Given Statement 1. MJH MJK Reason 1. HL 2. MJH MJK 2. All right angles are congruent (Euclid) 2. MNP ONP 2. AIA Congruence Theorem 3. H K 3. CPCTC 3. NP NP 4. MH MK ; HJ KJ MJH and MJK are right angles 3. Reflexive Property 4. Given 4. MNP ONP 4. SAS Created 6/2010 Printed 4/28/2017 Geometry Assignment 5E 18. Name _____________________________ Period ________ Date ________________ Given: B and D are right angles; C is the midpoint of BD ; AC EC 20. Given: AB CD , BC DA Prove: BAD DCB Prove: ABC EDC A B D C 2. B D 2. All right angles are congruent (Euclid) 3. BC DC 3. Definition of Midpoint 4. ABC EDC 4. SAS A D Statement 1. AB CD , BC AD Reason 1. Given 2. 2. Reflexive Property 3. BAD DCB 3. 21. M 19. Given: HJ KJ , MJH MJK Prove: MJH MJK H Statement 1. HJ KJ , MJK MJK Given the diagram below and a b . If the m1 3x 60 and m2 6x 30 , then what is the m1 and m2? For #19-20 fill in the missing part of the proof. J K Reason 1. Given 22. 3. MJH MJK C E Statement Reason 1. B and D are 1. Given right angles; C is the midpt of BD ; AC EC 2. MJ MJ B 2. In the diagram below, a b. Find m 1 and m2, if m1 = 5a and m2 = 2a + 12. t a 1 3. b 2 Created 6/2010 Printed 4/28/2017 Geometry Assignment 5E Name _____________________________ Period ________ Date ________________ For #23-24, is the argument valid or invalid? If it’s invalid, provide a counterexample. 28. Find the slope of the line parallel to the graph of y 23. If today is Friday, I’m eating fish for dinner. Today is Friday the 13th. Therefore, tonight I’m eating fish for dinner. 4 3 x– 2 3 . 29. What is the slope of the line perpendicular to the graph of 3x + 2y = 8? 30. Write the equation of a line that has a y-intercept of –3 and is parallel to 2 the graph of y x . 3 24. A square has four congruent sides. Polygon ABCD has four congruent sides. Therefore, polygon ABCD is a square. For #25-27, using the drawing below. R Q N P O 25. Name one line that is parallel to PO . 26. Name two lines that are perpendicular to PO . 27. Name two lines that are skew to PO . Created 6/2010 Printed 4/28/2017