Thursday, September 17, 2026

Geometric Challenge

Problem 1623: Two Adjacent Squares and Bounding Square Proof

Share your proof or solution in the comments below.
Target Audience: K-12, Honors Geometry, and College Mathematics Education.

In Problem 1623, we explore two adjacent squares constructed on a straight line. A bounding rectangle circumscribes both squares with its sides aligned parallel and perpendicular to an auxiliary segment. The challenge is to prove using pure triangle congruence that this bounding rectangle is strictly a square, and that its side length L equals the sum of the auxiliary segment length h and the altitude m drawn to it.
Explore the full theorem and illustrated diagram by clicking the image below.

Illustration of Geometry Problem 1623: Two Adjacent Squares and Bounding Square Proof
Click for additional details and full diagram.

How to contribute:
Post your step-by-step proof in the comments below. Feel free to:
  • Describe the theorems applied.
  • Share a link to your dynamic construction (GeoGebra, Desmos).
Be the first to submit a formal solution for this problem!
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