What type of triangle has no right angles and no two equal sides?

• A. Oblique triangle
• B. Acute triangle
• C. Obtuse triangle
• D. Right triangle

Answer: (A)

An oblique triangle is defined as a triangle that contains no right angles; it can either be acute, where all angles are less than 90 degrees, or obtuse, where one angle is greater than 90 degrees. However, the key characteristic of the oblique triangle in this question is that it does not have any right angles and also does not have two equal sides, which distinguishes it from isosceles triangles.

When discussing triangle types, acute triangles have all angles less than 90 degrees but can feature equal sides, while obtuse triangles contain one angle that is greater than 90 degrees and may also include equal sides. On the other hand, the right triangle inherently contains one 90-degree angle, which disqualifies it from being categorized as oblique. Therefore, an oblique triangle aptly fits the criteria of having no right angles and no two equal sides, making it the correct choice in this context.