38. Proof Prove that if two arcs of a circle are included between parallel chords, then the arcs are congruent.
39. Constructions Draw two segments. Label their lengths x and y. Construct the geometric mean of x and y. (Hint: Recall a theorem about a geometric mean.)

Standardized Test Prep

SAT/ACT

For Exercises 40 and 41, what is the value of each variable in ⊙ O ? circle dot o question mark

40. 
    1. 25
    2. 35
    3. 45
    4. 65
41. 
    1. 20
    2. 30
    3. 50
    4. 60
42. A large clock in a town square has a minute hand that is 10 ft long. Which value is the best estimate of how many degrees the minute hand moves from 4:00 to 4:40?
    1. 40 ° 40 degrees
    2. 120 ° 120 degrees
    3. 240 ° 240 degrees
    4. 400 ° 400 degrees

Extended Response

43. Is the following proof valid? If not, explain why, and then write a valid proof.

    Given: Quadrilateral ABCD, ∠ A ≅ ∠ C , B D ¯ angle , eh approximately equal to , angle c . comma , b d bar  bisects ∠ A B C angle eh b c

    Prove: ∠ A D B ≅ ∠ C D B angle , eh d b approximately equal to , angle c d b

    B D ¯ ≅ B D ¯ b d bar , approximately equal to , b d bar  by the Reflexive Property. Since B D ¯ b d bar  bisects ∠ A B C , angle eh b c comma  it also bisects ∠ A D C . angle eh d c .  So ∠ A D B ≅ ∠ C D B . angle , eh d b approximately equal to , angle c d b .

    

Mixed Review

See Lesson 12-2.

Algebra Find the value of x in ⊙ O , circle dot o comma  to the nearest tenth.

See Lesson 10-4.

47. The areas of two similar parallelograms are 20  cm 2 20 , cm squared  and 3.2  cm 2 . 3.2 , cm squared , .  What is the scale factor of the larger parallelogram to the smaller parallelogram?

Get Ready! To prepare for Lesson 12-4, do Exercises 48–51.

See Lessons 12-1–12-3.

In the diagram below, F E → f e vector  and F D → f d vector  are tangents to ⊙ C circle dot c  at E and D, respectively.

48. Find m D E ⌢ . m , modified d e with frown above , .
49. Find m ∠ A E C . m angle eh e c .
50. Find DF.
51. Find CE.

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