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.
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.
Click for additional details and full diagram.
How to contribute:
Post your step-by-step proof in the comments below. Feel free to:
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).
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