See Problem 4.

32. Proof Given: A B ¯ ║ D C ¯ , ∠ B ≅ ∠ D , eh b bar , box drawings double vertical . d c bar , comma . angle b approximately equal to angle d comma

    A B ¯ ≅ D C ¯ , B C ¯ ≅ A D ¯ eh b bar , approximately equal to . d c bar , comma . b c bar , approximately equal to . eh d bar

    Prove: Δ A B C ≅ Δ C D A cap delta eh b c approximately equal to cap delta c d eh

    

B Apply

33. If Δ D E F ≅ Δ L M N , cap delta d e f approximately equal to cap delta l m n comma  which of the following must be a correct congruence statement?
    1. D E ¯ ≅ L N ¯ d e bar , approximately equal to . l n bar
    2. F E ¯ ≅ N L ¯ f e bar , approximately equal to . n l bar
    3. ∠ N ≅ ∠ F angle n approximately equal to , angle f
    4. ∠ M ≅ ∠ F angle m approximately equal to , angle f

34. Reasoning Randall says he can use the information in the figure to prove Δ B C D ≅ Δ D A B . cap delta b c d approximately equal to cap delta d eh b .  Is he correct? Explain.

    

Algebra Δ A B C ≅ Δ D E F . cap delta eh b c approximately equal to cap delta d e f .  Find the measures of the given angles or the lengths of the given sides.

35. m ∠ A = x + 10 , m ∠ D = 2 x m angle , eh equals . x plus 10 comma . m angle . d equals 2 x
36. m ∠ B = 3 y , m ∠ E = 6 y − 12 m angle . b equals 3 , y comma m angle , e equals 6 y , minus 12
37. B C = 3 z + 2 , E F = z + 6 b c equals , 3 z plus 2 , comma e f equals , z plus 6
38. A C = 7 a + 5 , D F = 5 a + 9 eh c equals , 7 eh plus 5 , comma d f equals , 5 eh plus 9

39. Think About a Plan Δ A B C ≅ Δ D B E . cap delta eh b c approximately equal to cap delta d b e .  Find the value of x.

    

    • What does it mean for two triangles to be congruent?
    • Which angle measures do you already know?
    • How can you find the missing angle measure in a triangle?

Algebra Find the values of the variables.

40. 

    Δ A B C ≅ Δ K L M cap delta eh b c approximately equal to cap delta k l m

41. 

    Δ A C D ≅ Δ A C B cap delta eh c d approximately equal to cap delta eh c b

42. Complete in two different ways: Δ J L M ≅ cap delta j l m approximately equal to  __?__.

    

43. Open-Ended Write a congruence statement for two triangles. List the congruent sides and angles.
44. Proof Given: A B ¯ ⊥ A D ¯ ,   B C ¯ ⊥ C D ¯ ,   A B ¯ ≅ C D ¯ ,   A D ¯ ≅ C B ¯ ,   A B ¯ ‖ C D ¯ eh b bar , up tack , eh d bar , comma , b c bar , up tack , c d bar , comma , eh b bar , approximately equal to , c d bar , comma , eh d bar , approximately equal to , c b bar , comma , eh b bar . double vertical bar , c d bar

    Prove: Δ A B D ≅ Δ C D B cap delta eh b d approximately equal to cap delta c d b

    

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