31. Probability Below are six statements about the triangles below.

    

    • ∠ A ≅ ∠ X angle eh approximately equal to . angle x
    • A B ¯ ≅ X Y ¯ eh b bar , approximately equal to . x y bar
    • ∠ B ≅ ∠ Y angle b approximately equal to . angle y
    • A C ¯ ≅ X Z ¯ eh c bar , approximately equal to . x z bar
    • ∠ C ≅ ∠ Z angle c approximately equal to . angle z
    • B C ¯ ≅ Y Z ¯ b c bar , approximately equal to . y z bar

There are 20 ways to choose a group of three statements from these six. What is the probability that three statements chosen at random from the six will guarantee that the triangles are congruent?

Standardized Test Prep

SAT/ACT

32. Suppose R T ¯ ≅ N D ¯ r t bar , approximately equal to . n d bar  and ∠ R ≅ ∠ N . angle r approximately equal to . angle n .  What additional information do you need to prove that Δ R T J ≅ Δ N D F cap delta r t j approximately equal to cap delta n d f  by ASA?
    1. ∠ T ≅ ∠ D angle t approximately equal to , angle d
    2. ∠ J ≅ ∠ F angle j approximately equal to , angle f
    3. ∠ J ≅ ∠ D angle j approximately equal to , angle d
    4. ∠ T ≅ ∠ F angle t approximately equal to , angle f
33. You plan to make a 2 ft-by-3 ft rectangular poster of class trip photos. Each photo is a 4 in.-by-6 in. rectangle. If the photos do not overlap, what is the greatest number of photos you can fit on your poster?
    6. 4
    7. 24
    8. 32
    9. 36
34. Which of the following figures is a concave polygon?
    1. 
    2. 
    3. 
    4. 

Short Response

35. Write the converse of the true conditional statement below. Then determine whether the converse is true or false.
    • If you are less than 18 years old, then you are too young to vote in the United States.

Mixed Review

See Lesson 4-2.

Would you use SSS or SAS to prove the triangles congruent? Explain.

Get Ready! To prepare for Lesson 4-4, do Exercises 38 and 39.

See Lesson 4-1.

For Δ T I C ≅ Δ L O K , cap delta t i c approximately equal to cap delta l o k comma  list the indicated parts.

38. congruent corresponding angles
39. congruent corresponding sides

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