Geometry 6.1A Congruent Triangles Name __________________________ Completed:____ Correct:____ Grade:_______/10 Period____ Date_______________ For questions 1-5, given the Triangle Congruent Postulate draw the corresponding markings. 1. SSS 2. ASA 3. SAS 4. HL 5. AAS For questions 6-15, determine whether the following triangles can be proven congruent using the given information. If congruency can be proven, write a congruence statement and identify the postulate used to prove congruency. If not enough information is given, write not possible. A 6. 7. A B S C ΔABC ΔSBT, by ASA ΔABC ΔSBC, by SAS B S T C 8. A B 9. P ΔABD ΔCDB, by SSS NOT POSSIBLE A C D C Q B D 10. E 11. A ΔABC ΔEDC, by AAS A C ΔABC ΔADC, by HL C D B B 12. B 13. N ΔABD ΔCBD, by SAS or SSS A ΔABC ΔNMC, by AAS M C A C B D 14. A 15. A B B D ΔABC ΔADC, by SSS NOT POSSIBLE D C C For questions 16-25, state one additional fact that would make the triangles congruent and name the postulate. Write your answer as a conditional statement (IF, THEN). 16. 17. G B A If BC DF, then ΔABC ΔEDF by SAS If LH IK, then ΔGHL ΔKJI by SAS If C F, then ΔABC ΔEDF by AAS L If G J, then ΔGHL ΔKJI by ASA K If A E, then ΔABC ΔEDF by ASA H I If L I, then ΔGHL ΔKJI by AAS D C If AC EF, then ΔABC ΔEDF by HL E J F 18. Q 19. If MN NP, then ΔMNQ ΔPNO by HL If RS UV, then ΔSRT ΔVUW by ASA P If QN NO, then ΔMNQ ΔPNO by HL R S W If ST VW, then ΔSRT ΔVUW AAS If Q O, then ΔMNQ ΔPNO by AAS If RT UW, then ΔSRT ΔVUW AAS If M NPO, then ΔMNQ ΔPNO by AAS M O N U V T 20. A B 21. G H L K If CB DF, then ΔABC ΔEFD by SSS If HI KJ, then ΔGHI ΔLKJ by HL D If A E, then ΔABC ΔEFD by SAS If GH LK, then ΔGHI ΔLKJ by SAS C If H K, then ΔGHI ΔLKJ by AAS If I J, then ΔGHI ΔLKJ by ASA F I J E 22. 23. M A B X Y If NO PQ, then ΔMNO ΔRPQ by SSS If AB XY, then ΔMNO ΔRPQ by SSS N O If M R, then ΔMNO ΔRPQ by SAS If C Z, then ΔMNO ΔRPQ by SAS P Q C Z R F 24. 25. X Y E If XZ WV, then ΔXYZ ΔWUV by SAS D If EF CB, then ΔEFD ΔBCA by SSS A If Y U, then ΔXYZ ΔWUV by ASA If A D, then ΔEFD ΔBCA by SAS Z B W U If X W, then ΔXYZ ΔWUV by AAS C V Identify the triangle congruence postulates given below. 26. If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. SAS 27. If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent. HL 28. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. ASA 29. If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. SSS 30. If two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the triangles are congruent. AAS

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