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Pair of quadrilaterals (Posted on 2022-07-21) Difficulty: 4 of 5
Can two non-congruent quadrilaterals have the same four sides and same four angles?

Give an example or prove the task is never possible.

No Solution Yet Submitted by Jer    
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Some Thoughts Possible Solution | Comment 2 of 4 |
Name the two quadrilaterals A and B.  They can be convex.

Let A have sides a,b,c,d - all unequal - reading clockwise, with the angle between a and b equal to p, then q,r,s - all unequal - also reading clockwise.

In like manner, let B have sides a,d,b,c, and angles q,p,r,s.

Same sides, same angles, not congruent.

Edited on July 26, 2022, 11:59 pm
  Posted by broll on 2022-07-26 23:59:28

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