Geometry 1 omework 6.1b Name Name two triangles that are congruent by the ostulate. X W G I ell whether the ostulate can be used to prove the triangles congruent. If not, write not possible. 5. 30 0 30 0 ell whether the heorem or the ostulate can be used to prove the triangles congruent. If not, write not possible. 6. 7. 8. 9. I and GI. What else must you know to prove GI by: a. heorem b. ostulate What else must you know to prove the triangles congruent for the reason given. 10. heorem 1 ostulate O M N
1 ostulate 1 heorem W Z Y Write a congruence statement for each pair of triangles. Name the postulate or theorem that justifies your statement. 1 M 15. 16. W O N Z Y If the two triangles are congruent for the given conditions, write a congruence statement. ustify your conclusion. 17.,, O X 18.,, O X X O 19. O X, X, O 20. O X,, O X, What additional information do you need to prove the triangles congruent by L heorem? 2 L and 2 X and L X
2 Y and Y 2 and G G Y 25. and 26. and N N ell whether the L heorem can be used to prove the two triangles congruent. If so, explain. If not, write not possible. 27. 28. is the midpoint of M W or what values of x and y are the triangles congruent by the L heorem? 29. 30. x x + 3 3y y + 1 3y + x y + 5 x + 5 y x Multiple hoice ircle the correct answer. Which additional congruence statement could be used to prove that by the L heorem? 3 Given:....
Which additional congruence statement could be used to prove that by the L heorem? 3 Given:.... 3 Which of the following postulates or theorem can be used to prove the two triangles congruent?. ostulate. ostulate. ostulate. L heorem 3 Given:, rove: tatements ; easons 35. Given:, and are right angles rove: tatements, and are right angles easons and are right triangles
36. Given:,, is the midpoint of rove: tatements,, is the midpoint of easons and are right angles. ertical angles are 5. 5. 6. 6. 37. Given:, and are right angles rove: tatements, and are right angles and are right triangles easons 38. Given: bisects, rove: tatements bisects, easons
39. Given: L LM, L, M L rove: LM L tatements L LM, L, M L L easons LM and L are right angles efinition of a right triangle eflexive roperty 5. LM L 5. M 40. Given: G, G, I is the midpoint of rove: IG I G I tatements easons G, G, I is the midpoint of efinition of perpendicular IG and I are right triangles I I 5. 5. L heorem nswers XW Yes Yes 5. Yes 6. heorem 7. ostulate 1 WZ YWZ or WZ WZY 1 MO NMO ; ostulate 15. ; heorem 16. ZY WY ; heorem 17. X O ; heorem 8. Not ossible 9. a. b. G 10. 1 M N 1 18. he triangles are not congruent because no sides are congruent.
19. X O ; ostulate 20. he triangles are not congruent because the congruent angles are not included angles. 2 and are right angles 2 X or X 2 Y or Y 2 ight angles are needed, either and G or and G 25. 26. N 27. Yes; because of the definition of midpoint. herefore, the hypotenuse and leg of the right triangle are congruent. 28. Yes; M M by the reflexive property and MW is a right angle since MW 29. x = 3; y = 2 30. x = 1; y = 3 3 3 3 3 Given If lines, then alternate interior angles congruent. eflexive roperty heorem 35. Given efinition of a right triangle eflexive roperty L heorem 36. Given efinition of perpendicular ll right angles are congruent 5. efinition of midpoint 6. ostulate 37. Given efinition of a right triangle eflexive roperty L heorem 38. Given efinition of bisect eflexive roperty heorem 39. Given efinition of perpendicular LM and L are right s L L 5. L heorem 40. Given GI and I are right angles efinition of a right triangle efinition of midpoint 5. IG I