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SquareByAdjacentMidpointsImage.png

Instruction: Construct a square, given two midpoints of adjacent sides.

Goal: 7L 10E

Available tools:

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

Pack: Delta

Previous level: 4.9

Next level: 4.11

7L solution[]

Let A and B be the given midpoints.

  1. Construct line AB
  2. Construct the perpendicular to AB from A
  3. Construct the angle bisector of ∠BAC with C an arbitrary point on the perpendicular
  4. Construct the perpendicular to that angle bisector through B, intersecting AC at D
  5. Construct the circle with center B and radius BD, intersecting BD at E and AC at F
  6. Construct the perpendicular bisector of BE
  7. Construct the perpendicular to the angle bisector of ∠BAC through F

10E solution[]

Let A and B be the given midpoints.

  1. Construct line AB
  2. Construct the perpendicular bisector of AB, intersecting AB at C
  3. Construct the circle with center C and radius AC, intersecting the perpendicular bisector of AB at D and E
  4. Construct line AD
  5. Construct line BD
  6. Construct the circle with center E and radius DE, intersecting AD at F, DE at G and BD at H
  7. Construct line FG
  8. Construct line GH

2V solution[]

From the 7L solution: Let G be the intersection of the perpendicular bisector of BE and AB

  1. Construct the perpendicular to the perpendicular bisector from G
  2. Construct the line BF
  3. Construct the perpendicular to BF through A
  4. Construct the perpendicular to the previous perpendicular through D

From the 10E solution: Let I be the intersection of FG and AB, and J the intersection of GH and AB

  1. Construct the perpendicular to FI from I
  2. Construct the perpendicular to HJ from J
  3. Construct line AE
  4. Construct line BE

Explanation[]

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