A Step-by-Step Guide to Constructing a Triangle from Its Sides

• A straightedge or ruler.
• A compass.
• A pencil.

Examples

Practice Questions:

1. What conditions must three side lengths fulfill to construct a triangle?
2. After constructing a triangle using three side lengths, how can you ascertain if it’s a right triangle?
3. Using side lengths \(4 \text{ cm}\), \(6 \text{ cm}\), and \(11 \text{ cm}\), is triangle construction feasible?

1. The sum of any two side lengths must exceed the third. This principle is termed the triangle inequality theorem.
2. Post-construction, apply the Pythagorean theorem to all sides. If the square of the longest side equals the sum of the squares of the other two, it’s a right triangle.
3. No. The combined lengths of the shorter sides, \(4 + 6 = 10 \text{ cm}\), falls short of the longest side’s length \(11 \text{ cm}\). Triangle construction isn’t possible with these measurements due to the triangle inequality theorem.

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