Algebra Find the values of m and n.

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C Challenge

Coordinate Geometry For each pair of points, there are six points that could be the third vertex of an isosceles right triangle. Find the coordinates of each point.

33. (4, 0) and (0, 4)
34. (0, 0) and (5, 5)
35. (2, 3) and (5, 6)
36. Reasoning What measures are possible for the base angles of an acute isosceles triangle?

Standardized Test Prep

SAT/ACT

37. In isosceles Δ A B C , cap delta eh b c comma  the vertex angle is ∠ A . angle eh .  What can you prove?
    1. A B = C B eh b equals c b
    2. m ∠ B = m ∠ C m angle b equals m angle c
    3. ∠ A ≅ ∠ B angle eh approximately equal to angle b
    4. B C ¯ ≅ A C ¯ b c bar , approximately equal to . eh c bar
38. Δ L M N ≅ Δ P Q R . cap delta l m n approximately equal to cap delta p q r .  What is LM?
    6. 3
    7. 4
    8. 8
    9. 10

    

39. What is the exact area of the base of a circular swimming pool with diameter 16 ft?
    1. 1018.29 ft 2 1018.29 . ft squared
    2. 1018.3 ft 2 1018.3 . ft squared
    3. 64 π ft 2 64 pi , ft squared
    4. 256 π ft 2 256 pi , ft squared
40. Short Response Suppose Δ A B C cap delta eh b c  and Δ D E F cap delta d e f  are nonright triangles. If ∠ B ≅ ∠ E angle b approximately equal to angle e  and A B ¯ ≅ D E ¯ , eh b bar , approximately equal to . d e bar , comma  what else do you need to know to prove Δ A B C ≅ Δ D E F ? cap delta eh b c approximately equal to cap delta d e f question mark  Explain.

Mixed Review

See Lesson 4-4.

41. m ∠ R = 59 , m ∠ T = 93 = m ∠ H , m ∠ V = 28 , m angle . r equals 59 comma . m angle , t equals , 93 equals , m angle h comma m angle . v equals 28 comma  and R T = G H . r t equals g h .  What, if anything, can you conclude about RC and GV? Explain.

    

See Lesson 2-1.

42. Find the pattern of the sequence M, T, W, T, F, … Then find the next two terms.

Get Ready! To prepare for Lesson 4-6, do Exercises 43 and 44.

See Lesson 4-2.

Can you conclude that the two triangles are congruent? Explain.

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