For Exercises 43 and 44, x and y are integers such that 1 < x < 5 less than bold italic x less than 5  and 2 < y < 9 . 2 less than bold italic y less than 9 .

43. The sides of a triangle are 5 cm, x cm, and y cm. List all possible (x, y) pairs.
44. Probability What is the probability that you can draw an isosceles triangle that has sides 5 cm, x cm, and y cm, with x and y chosen at random?

45. Proof Prove the Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

    Given: Δ A B C cap delta eh b c

    Prove: A C + C B > A B eh c plus . c b greater than eh b

    

    (Hint: On B C → , b c vector , comma  mark a point D not on B C ¯ , b c bar , comma  so that D C = A C . d c equals eh c .  Draw D A ¯ d eh bar  and use Theorem 5-11 with Δ A B D . cap delta eh b d . )

Standardized Test Prep

SAT/ACT

GRIDDED RESPONSE

46. The figure shows the walkways connecting four dormitories on a college campus. What is the greatest possible whole-number length, in yards, for the walkway between South dorm and East dorm?
47. What is the length of a segment with endpoints A ( − 13 , − 16 ) eh open negative 13 comma negative 16 close  and B ( − 9 , − 13 ) ? b open negative 9 comma negative 13 close question mark
48. How many sides does a convex quadrilateral have?
49. ∠ 1 angle 1  and ∠ 2 angle 2  are corresponding angles formed by two parallel lines and a transversal. If m ∠ 1 = 33 x + 2 m angle , 1 equals . 33 x plus 2  and m ∠ 2 = 68 , m angle , 2 equals 68 , comma  what is the value of x?

Mixed Review

See Problem 5-5.

Write the first step of an indirect proof of the given statement.

50. The side is at least 2 ft long.
51. Δ P Q R cap delta p q r  has two congruent angles.

See Lesson 4-2.

52. You know that A B ¯ ≅ X Y ¯ , B C ¯ ≅ Y Z ¯ , eh b bar , approximately equal to . x y bar , comma . b c bar , approximately equal to . y z bar , comma  and C A ¯ ≅ Z X ¯ . c eh bar , approximately equal to . z x bar , .  By what theorem or postulate can you conclude that Δ A B C ≅ Δ X Y Z ? cap delta eh b c approximately equal to cap delta x y z question mark

Get Ready! To prepare for Lesson 5-7, do Exercises 53–55.

See Problem 3-5.

Use the figure below.

53. What is m ∠ P ? m angle p question mark
54. What is m ∠ D ? m angle d question mark
55. Is it possible for AW to equal OG?

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