The angles in an actual triangle-shaped traffic sign all have measures of 60°. The angles in a scale drawing of the sign all have measures of 60°. Explain how you can use this information to decide whether three given angle measures can be used to form a unique triangle or more than one triangle.
The figure on the left shows a line segment 2 inches long forming a 45° angle with a dashed line whose length is not given. The figure on the right shows a compass set at a width of \(1\frac{1}{2}\) inches with its point on the top end of the 2-inch segment. An arc is drawn intersecting the dashed line twice.
Explain how you can use this figure to decide whether two sides and an angle not included between them can be used to form a unique triangle, more than one triangle, or no triangle.
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