Geometry 1A Homework 6.1b. Tell whether the ASA Postulate can be used to prove the triangles congruent. If not, write not possible
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1 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 ell whether the heorem or the ostulate can be used to prove the triangles congruent. If not, write not possible 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
2 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 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
3 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 is the midpoint of M W or what values of x and y are the triangles congruent by the L heorem? 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:....
4 Which additional congruence statement could be used to prove that by the L heorem? 3 Given: 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
5 36. Given:,, is the midpoint of rove: tatements,, is the midpoint of easons and are right angles. ertical angles are Given:, and are right angles rove: tatements, and are right angles and are right triangles easons 38. Given: bisects, rove: tatements bisects, easons
6 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 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 M N he triangles are not congruent because no sides are congruent.
7 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 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 = x = 1; y = 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
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