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How to Construct an Acute Triangle. To construct an acute triangle, simple first construct an angle that is less than 90 degrees and greater than 0 degrees. This will create two sides of your triangle. Then cnstruct a third line intersecting your first two, and you have an acute triangle.
In either case, notice that the right angle becomes an acute angle. This allows us to state variation #2 on the Pythagorean Theorem: Notice: an acute triangle is a triangle in which all three angles are acute. In any triangle, at least two of the angles must be acute. In an acute triangle, even the largest angle is acute. Summary. We can combine all this information in one place. Suppose a triangle has three sides such that a < b < c. Then: