4 Circle the letter of each true statement below.
a. An obtuse triangle does not have acute angles.
b. A scalene triangle can be isosceles.
c. Equilateral triangles are always acute.
d. Isosceles triangles may also be equilateral.
e. Right triangles are scalene or isosceles.
Answer
e. True: Right triangles can be scalene (e.g. 3-4-5 triangle) or isosceles (e.g. \(1-1-\sqrt{2}\) triangle).
Step 1 ：a. False: An obtuse triangle has one obtuse angle and two acute angles.
Step 2 ：b. False: A scalene triangle has all sides of different lengths, while an isosceles triangle has at least two sides of equal length.
Step 3 ：c. True: Equilateral triangles have all sides equal, and all angles measure \(60^\circ\), which are acute angles.
Step 4 ：d. True: Isosceles triangles may be equilateral, as the requirement for an isosceles triangle is to have at least two sides equal.
Step 5 ：e. True: Right triangles can be scalene (e.g. 3-4-5 triangle) or isosceles (e.g. \(1-1-\sqrt{2}\) triangle).
