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Cut2RectanglesDetailed.7ff7b16d8eaf942a3aa4ff1004986d18.png

Instruction: Construct a line that cuts each of the rectangles into two parts of equal area.

Goal: 5L 5E

Available tools:

  • Move
  • Point
  • Line
  • Circle
  • Perpendicular Bisector
  • Perpendicular
  • Angle Bisector
  • Intersect

Pack: Delta

Previous level: 4.4

Next level: 4.6

5L 5E solution[]

Given the rectangles ABCD and EFGH.

  1. Construct line AC, a diagonal of the first rectangle
  2. Construct line BD, the other diagonal, intersecting the previous diagonal at I
  3. Construct line EG, a diagonal of the second rectangle
  4. Construct line FH, the other diagonal, intersecting the previous diagonal at J
  5. Construct line IJ

Explanation[]

Any straight line through the center of a rectangle divides the rectangle into equivalent halves (180o rotational symmetry around its center). Find each rectangle's center and draw one line through both points.

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