A, B, C, and D are points of concurrency for the triangle. Determine whether each point is a circumcenter, incenter, centroid, or orthocenter. Explain.

37. 
38. 
39. History In 1765, Leonhard Euler proved that, for any triangle, three of the four points of concurrency are collinear. The line that contains these three points is known as Euler's Line. Use Exercises 37 and 38 to determine which point of concurrency does not necessarily lie on Euler's Line.

Standardized Test Prep

SAT/ACT

For Exercises 40 and 41, use the figure below.

40. If C R = 24 , c r equals 24 . comma  what is KR?
    1. 6
    2. 8
    3. 12
    4. 16
41. If T R = 12 t r equals 12  what is CP?
    6. 16
    7. 18
    8. 24
    9. 36

Extended Response

42. The orthocenter of a triangle lies outside the triangle. Where are its circumcenter, incenter, and centroid located in relation to the triangle? Draw and label diagrams to support your answers.

Mixed Review

See Problem 5-3.

Is X Y ¯ x y bar  a perpendicular bisector, an angle bisector, or neither? Explain.

Get Ready! To prepare for Lesson 5-5, do Exercises 45–47.

See Problem 2-2.

Write the negation of each statement.

45. Two angles are congruent.
46. You are not 16 years old.
47. m ∠ A < 90 m angle , eh less than 90

Table of Contents