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LozengeDetailed.bec74b2339c825fa6a6c14b813c5433f.png

Instruction: Construct a rhombus with the given side and an angle of 45° in a vertex.

Goal: 5L 7E

Available tools:

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

Pack: Gamma

Previous level: 3.7

Next level: 3.9

5L solution[]

Given the side AB.

  1. Construct the perpendicular to AB from A; let C be a distinct arbitrary point on that perpendicular
  2. Construct the angle bisector of ∠BAC
  3. Construct the circle with center A and radius AB, intersecting the angle bisector at D and line AC at E with E on the opposite side of C from A
  4. Construct the perpendicular to AC through D
  5. Construct line BE

7E solution[]

Given the side AB.

  1. Construct the circle with center A and radius AB
  2. Construct the circle with center B and radius AB, intersecting circle A at C and D
  3. Construct line CD, intersecting AB at E
  4. Construct the circle with center E and radius AE, intersecting CD at F and G
  5. Construct line AF, intersecting circle A at H
  6. Construct line BG, intersecting circle B at I on the same side as H relative to AB
  7. Construct line HI

4V solution[]

From the 5L solution:

  1. Construct the perpendicular to AD through B
  2. Construct the perpendicular to AD from A; let F be the diametrical opposite of the intersection of circle A with the perpendicular to AC through D on circle A
  3. Construct the perpendicular to CD through F

From the 7E solution: Let J be the other intersection of line AF with circle A and K the other intersection of line BG with circle B.

  1. Construct line JK
  2. Construct line AG
  3. Construct line BF

Explanation[]

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