What is an isosceles triangle?

What is an isosceles triangle?

• A. One angle 90 degrees.
• B. THREE sides same length, THREE angles equal.
• C. No sides same length.
• D. Two sides same length, TWO angles are same measure.

Answer: (D)

An isosceles triangle is defined by two sides having equal length, and the angles opposite those equal sides are equal as well. That direct relationship is captured by saying two sides are the same length and the two angles opposite those sides have the same measure. In any triangle, equal sides imply equal opposite angles, so this combination is exactly what characterizes an isosceles triangle. Context helps: you can have a right triangle with a 90-degree angle that isn’t isosceles if the other two sides aren’t equal, and a triangle where all three sides and all three angles are equal—that’s an equilateral triangle, a special case of isosceles but not the general definition. A triangle with no equal sides is scalene. So the best description is the one that states two sides are equal and the two opposite angles are equal.

An isosceles triangle is defined by two sides having equal length, and the angles opposite those equal sides are equal as well. That direct relationship is captured by saying two sides are the same length and the two angles opposite those sides have the same measure. In any triangle, equal sides imply equal opposite angles, so this combination is exactly what characterizes an isosceles triangle.

Context helps: you can have a right triangle with a 90-degree angle that isn’t isosceles if the other two sides aren’t equal, and a triangle where all three sides and all three angles are equal—that’s an equilateral triangle, a special case of isosceles but not the general definition. A triangle with no equal sides is scalene.

So the best description is the one that states two sides are equal and the two opposite angles are equal.