There are two ways to classify triangles. The first way deals with the size of the largest angle in the triangle.
Obtuse triangle: A triangle is obtuse if the largest angle is greater than 90 degrees in measure. If the sides are given as a, b and c, where c is the longest side, if a^2 + b^2 < c^2, the triangle is obtuse.
Right triangle: If the largest angle is exactly 90 degrees in measure, the triangle is a right triangle. If the sides are given as a, b and c, where c is the longest side, a^2 + b^2 = c^2 means we have a right triangle. This is known as the Pythagorean Theorem.
Acute triangle: If the largest angle is less than 90 degrees, the triangle is called an acute triangle. If the sides are given as a, b and c, where c is the longest side, a^2 + b^2 > c^2 means we have an acute triangle.
The other method of classification has to do with having angles of the same measure or sides of the same length.
Equilateral triangle: All three angles have the same measure, 60 degrees. All three sides are the same length.
Isosceles triangle: At least two sides have the same measure, which also means two angles must have the same measure. Technically, and equilateral triangle is still isosceles, but it is a special case and we usually name it by the more specific name.
Scalene triangle: All three sides are different lengths, and all three angles are different measure.
1) Can a triangle be both a right triangle and an isosceles triangle?
2) A triangle has side lengths 3, 3 and 4. What are its two classifications?
3) A triangle has two angles, 70 degrees and 15 degrees. What are its two classifications?
4) An isosceles triangle has one angle of measure 40 degrees. What are the two possible sets of angle measures and classify both as acute, right or obtuse.
5) A triangle has side lengths 5, 12 and 13. What are its two classifications?
Answers in the comments.