In which shape do all sides have equal length and all angles have equal measure?

The correct response describes a shape where all sides are of the same length and all angles are equal, which defines an equilateral triangle. In geometry, an equilateral triangle is a specific type of triangle that has three sides of equal length and three angles that each measure 60 degrees, thus meeting the criteria for equality in both sides and angles.

The other shapes mentioned do not meet both conditions. A rectangle has opposite sides that are equal in length, but not all four sides are equal, and its angles measure 90 degrees, not all equal angles. A pentagon, which has five sides, does not necessarily have equal side lengths or equal angles unless it is a regular pentagon, which is not specified in the question. A trapezoid generally has only one pair of parallel sides and does not have equal length for all sides or equal angle measures.

This clarity on properties is essential for distinguishing between various geometric figures and understanding their defining characteristics.