Chapter 3.1, Problem 29WE

To determine

To find: To use theorem 3.1 to prove $CD\left|\right|IJ$ , in given figure.

Answer to Problem 29WE

Two line segments

  $\overline{CD}$ and $\overline{IJ}$ are parallel to each other.

Explanation of Solution

Given information: In below figure, planes $AFEDCB$ and $GLKJIH$ are parallel to each other.

  

Concept used: Theorem 3.1 to be used, states that, “If two parallel planes are cut by a third plane, then the lines of intersection are parallel.”

Calculation: In given figure, two parallel planes $AFEDCB$ and $GLKJIH$ are cut by another plane $CDJI$ , so that the lines passing from points C and D as well as lines passing from points I and J will be lines of intersection here. And hence by above statement of theorem 3.1, these two lines of intersection will be parallel to each other. Thus,

  $CD\left|\right|IJ$

Conclusion: Thus, as line segments $CD$ and $IJ$ are of plane $CDJI$ that intersects two parallel planes $AFEDCB$ and $GLKJIH$ , so these two line segments will always be parallel to each other.