Complete the following questions. The answers are listed below for you to check yourself.

Review Questions

R,S,T,U are midpoints of sides of triangles \triangle XPO and \triangle YPO.

Complete the following:

  1. If OP = 12, then RS= ___ and TU = ___.
  2. If RS = 8, then TU = ____.
  3. If RS = 2x and OP = 18, then x =___and TU = ___.
  4. If OP = 4x and RS = 6x-8, then x = _____.
  5. Consider triangle \triangle XYZ with vertices X(1,1), Y(5,5), Z(3,9) and midpoint M on \overline{XZ}.

    1. Find the coordinates of point M.
    2. Use the Midsegment Theorem to find the coordinates of the point N on side \overline{YZ} that makes \overline{MN} the midsegment.
  6. For problem 5, describe another way to find the coordinates of point N that does not use the Midsegment Theorem.

In problems 7-8, the segments join the midpoints of two sides of the triangle. Find the values of x and y for each problem.

  3. In triangle \triangle XYZ, sides \overline{XY}, \overline{YZ}, and \overline{ZX} have lengths 26,38 and 42 respectively. Triangle \triangle RST is formed by joining the midpoints of \triangle XYZ. Find the perimeter of \triangle RST.
    1. For the original triangle \triangle XYZ of 9, find its perimeter and compare to the perimeter of \triangle RST.
    2. Can you state a relationship between a triangle’s perimeter and the perimeter of the triangle formed by connecting its midsegments?

Review Answers

  1. RS = 6 and TU = 6
  2. TU = 8
  3. x = \frac{9}{2}, TU = 9
  4. x = 2
    1. M(2,5)
    2. N(4,7)
  6. Find midpoint M and then the slope of \overline{XY}. Find the line through M parallel to \overline{XY} (line l_1). Find the equation of the line that includes \overline{YZ} (line l_2). Find the intersection of lines l_1 and l_2.
  7. x = 5, y = 3
  8. x = 7, y = \frac{7} {2}
  9. P = 53
    1. The perimeter of \triangle XYZ is 106. The perimeter of \triangle RST is 53.
    2. The perimeter of the midsegment triangle will always be half the perimeter of the original triangle.
Last modified: Monday, May 10, 2010, 7:44 PM