Uniqueness of Triangle Construction III

Uniqueness of Triangle Construction III

Introduction

Some combinations of side lengths or angle measures make it impossible to construct a triangle. Checking the given measurements helps recognize when no triangle can be formed and explains why the constru...

Carlos wants to build a triangular frame using three rods measuring 2 inches, 3 inches, and 6 inches.

Carlos places the two shorter rods at the endpoints of the 6-inch rod. But the shorter rods cannot reach each other, and the frame cannot close, so a triangle cannot be formed.

The two shorter rods measure 2 inches and 3 inches. Thei...