A carpenter’s measuring tricks fascinate me. These guys have figured out ways to do math without all that pesky math getting in the way.
The most recent trick I learned is a great geometry class problem: how to divide anything into equally-sized sections. For example, suppose I want to place the handles exactly 1/4 the way from each end on this drawer front.
I’ve also read that cabinetmakers use this trick to set equally-spaced dovetail joints.
You can prove the “trick” using a triangle congruence theorem1.
Better yet, there’s a tool to do the same division. Again, you can prove the tool works with a triangle congruence theorem2.
Edit: I took this in to my 9th grade students who are repeating Georgia’s Math 1 class (it’s a combination of algebra and geometry) and they crushed my excitement. Perhaps it’s just the crowd but those guys shot me down in flames. Zero interest in a cool trick. Zero interest in why it works. Honestly, I had higher hopes for “hey guys, you can divide anything — any size — into equal segments with only mental math.”
Georgia Performance Standard: MM1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons. c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).
1 ASA, as shown here