20. Designs Rangoli is a colorful design pattern drawn outside houses in India, especially during festivals. Vina plans to use the pattern below as the base of her design. In this pattern, R U ¯ , S V ¯ , r u bar , comma . s v bar , comma  and Q T ¯ q t bar  bisect each other at O. R S = 6 , R U = 12 , R U ¯ ≅ S V ¯ , S T ¯ | | R U ¯ , r s , equals 6 comma . r u , equals 12 comma . r u bar , approximately equal to . s v bar , comma . s t bar , vertical line vertical line . r u bar , comma  and R S ¯ | | Q T ¯ . r s bar , vertical line vertical line . q t bar , .  What is the perimeter of the hexagon?

    

C Challenge

In the diagram below, B A ¯ ≅ K A ¯ b eh bar , approximately equal to , k eh bar  and B E ¯ ≅ K E ¯ . b e bar , approximately equal to . k e bar , .

21. Proof Prove: S is the midpoint of B K ¯ . b k bar , .
22. Proof Prove: B K ¯ ⊥ A E ¯ b k bar , up tack , eh e bar

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

For Exercises 23 and 24, use the diagram below. T M ¯ ⊥ B D ¯ t m bar . up tack , b d bar  and T M ¯ t m bar  bisects ∠ B T D angle b t d  and ∠ A T C . angle eh t c .

23. Suppose B D = 17 b d equals 17  and A M = 5 . eh m equals 5 .  What is the length of C D ¯ ? c d bar , question mark
24. Suppose m ∠ A T C = 64 , m angle eh t c . equals 64 comma  and m ∠ B T A = 16 . m angle b t eh . equals 16 .  What is m ∠ B ? m angle b question mark
25. Two parallel lines q and s are cut by a transversal t . ∠ 1 t . angle 1  and ∠ 2 angle 2  are a pair of alternate interior angles and m ∠ 2 = 38 . ∠ 1 m angle . 2 equals 38 . . angle 1  and ∠ 3 angle 3  are vertical angles. What is m ∠ 3 ? m angle 3 question mark
26. Δ A B C cap delta eh b c  has vertices A(1, 9), B(4, 3), and C(x, 6). For what value of x is Δ A B C cap delta eh b c  a right triangle with right ∠ B ? angle b question mark

Mixed Review

See Lesson 4-3.

For Exercises 27 and 28, tell the postulate or theorem that you can use to prove the triangles congruent.

See Lesson 3-5.

Get Ready! To prepare for Lesson 4-5, do Exercises 29–32.

29. What is the side opposite ∠ A B C ? angle eh b c question mark
30. What is the angle opposite side A B ¯ ? eh b bar , question mark
31. What is the angle opposite side B C ¯ ? b c bar , question mark
32. Find the value of x.

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