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

To construct a triangle from three given sides, draw one side as a base, then swing an arc from each endpoint with the other two lengths. Where the arcs cross is the third vertex, provided the three lengths satisfy the triangle inequality.

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

Worked examples: constructing a triangle from three sides

Practice questions on triangle construction

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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