C Challenge

30. Reasoning Explain why the circumcenter of a right triangle is on one of the triangle's sides.

Determine whether each statement is always, sometimes, or never true. Explain.

31. It is possible to find a point equidistant from three parallel lines in a plane.
32. The circles inscribed in and circumscribed about an isosceles triangle have the same center.

Standardized Test Prep

SAT/ACT

33. Which of the following statements is false?
    1. The bisectors of the angles of a triangle are concurrent.
    2. The midsegments of a triangle are concurrent.
    3. The perpendicular bisectors of the sides of a triangle are concurrent.
    4. Four lines intersecting in one point are concurrent.
34. What type of triangle is Δ P U T ? cap delta p u t question mark

    

    6. right isosceles
    7. acute isosceles
    8. obtuse scalene
    9. acute scalene

35. Which statement is logically equivalent to the following statement?

    If a triangle is right isosceles, then it has exactly two acute angles.

    1. If a triangle is right isosceles, then it has one right angle.
    2. If a triangle has exactly two acute angles, then it is right isosceles.
    3. If a triangle does not have exactly two acute angles, then it is not right isosceles.
    4. If a triangle is not right isosceles, then it does not have a right angle.

Short Response

36. Refer to the figure below above. Explain in two different ways why M V ¯ m v bar  is the angle bisector of ∠ K V R . angle k v r .

    

Mixed Review

See Lesson 5-2.

Use the figure below for Exercises 37 and 38.

37. Find the value of x.
38. Find the length of A D ¯ . eh d bar , .

Get Ready! To prepare for Lesson 5-4, do Exercises 39 and 40.

See Lesson 1-7.

Find the coordinates of the midpoint of A B ¯ eh b bar  with the given endpoints.

39. A ( 3 , 0 ) , B ( 3 , 16 ) eh open 3 comma 0 close comma b open 3 comma 16 close
40. A ( 6 , 8 ) , B ( 4 , − 1 ) eh open 6 comma 8 close comma b open 4 comma negative 1 close

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