How do you classify a triangle if two of the sides are the same? (e.g. 4,5,5)

Question

mathslover · Answer

The triangle having two sides equal in length is called an Isosceles Triangle.

mathslover · Answer

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anonymous · Answer

According to the book, it has to be acute, obtuse or right. (sorry, forgot to mention that)

mathslover · Answer

Well Acute, obtuse and right triangles are classified on the basis of angles. So not sure what is the relation of side's length with Acute, Obtuse and Right.
Sorry

anonymous · Answer

With the use of the Pythagorean theorem(a^2+b^2=c^2), you're suppose to make the largest side c but how do you do that if both sides are equal?

anonymous · Answer

$$a^2+b^2=c^2$$

whpalmer4 · Answer

If a triangle has exactly two equal sides, it must be an isosceles triangle.  However, knowing that alone is not sufficient to classify it into acute, obtuse, or right.  If you know all three sides, however, you can determine which of the three types it is.

If the sum of the squares of the lengths of the two shorter sides equals the square of the length of the longest side, then you have a right triangle, because the Pythagorean theorem is only satisfied in a right triangle.

If the sum of the squares of the lengths of the two shorter sides is greater than the square of the length of the longest side, then you have an acute triangle.

If the sum of the squares of the lengths of the two shorter sides is less than the square of the length of the longest side, then you have an obtuse triangle.