Which shape is a parallelogram but not a rhombus?…

Mathematics Questions

Which shape is a parallelogram but is NOT a rhombus?

Short Answer

A parallelogram has four sides with opposite sides being equal and parallel, totaling 360 degrees in interior angles. A rhombus, a specific type of parallelogram, also has four equal sides. To identify a parallelogram specifically, options can be eliminated based on these characteristics, confirming that the remaining option is a parallelogram but not a rhombus.

Step-by-Step Solution

Step 1: Understand the Parallelogram

A parallelogram is a polygon that has four sides, where the opposite sides are both parallel and equal in length. The interior angles of a parallelogram total 360 degrees. This means that each angle can have varying measures, but they must all add up to 360 degrees.

Step 2: Identify the Rhombus

A rhombus is a specific type of parallelogram that also has four sides, but with the additional feature that all four sides are of equal length. Like the parallelogram, the total interior angle is also 360 degrees. However, the key difference lies in the equality of the sides, which distinguishes a rhombus from other parallelograms.

Step 3: Eliminate Incorrect Options

To determine the correct option regarding the shape in question, we can eliminate choices based on their characteristics:

  • Options C and D can be disregarded as their opposite sides are not parallel.
  • Option A is also eliminated because it describes a shape where all sides are equal, which indicates a rhombus.
  • This leaves us with option B, confirming that the shape is a parallelogram but not a rhombus.

Related Concepts

Parallelogram

A polygon with four sides where opposite sides are parallel and equal in length, and the interior angles total 360 degrees.

Rhombus

A specific type of parallelogram in which all four sides are of equal length while maintaining the total interior angle of 360 degrees.

Interior Angles

Angles formed inside a polygon, which in the case of a quadrilateral like a parallelogram or rhombus, sums up to 360 degrees.

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