A significant segment of mathematics known as geometry is wholly based on the studies of different shapes. These shapes are everywhere, but people barely notice them.

Table of Contents

Geometry elaborates these shapes and introduces students to the formulas and techniques to understand them. Isosceles Trapezium and Trapezium are also two types of shapes that might look alike but are very different.

**Isosceles Trapezium vs Trapezium**

**The main difference between an isosceles Trapezium and a Trapezium is that Isosceles Trapezium can be cut into two symmetrical halves by a bisector. It is one type of Trapezium. On the other hand, Trapezium can not be cut into two identical halves, but it has a pair of parallel lines. A trapezium is generally an irregular square because they have some properties of a square. **

Isosceles Trapezium, also known as Isosceles Trapezoid, is a two-dimensional shape studied in geometry. It is considered to be a convex quadrilateral that has a bisecting line.

This line bisects the Isosceles Trapezium and creates two symmetrical Trapezium. It is one quadrilateral with four vertices and four edges.

Isosceles Trapezium also has an area and perimeter to be measured.

Trapezium, also known as Trapezoid, is another two-dimensional shape studied in geometry. It is a type of quadrilateral because it has four vertices and four edges.

A Trapezium is divided into five classes that are scalene, Isosceles, obtuse, acute, and right Trapezium. It has a pair of parallel lines and the properties of a convex polygon.

**Comparison Table Between Isosceles Trapezium and Trapezium**

Parameters Of Comparison | Isosceles Trapezium | Trapezium |

Meaning | A quadrilateral shape with uneven parallel sides or lines is known as Isosceles Trapezium. | A quadrilateral shape that has one pair of parallel sides or lines is called Trapezium. |

Other names | In North and South American English, an isosceles Trapezium is called Isosceles Trapezoid. | In North and South American English, a Trapezium is called Trapezoid. |

Types | Isosceles Trapezium has not been divided into any division because it already belongs to Trapezium. | A Trapezium is subcategorized into five categories that are acute, obtuse, isosceles, right, and scalene Trapezium. |

Features | An isosceles Trapezium is made of two identical Trapezium that can be observed by a bisector in between. | A Trapezium is one of the most irregular quadrilateral shapes which is generally associated with fields. |

Formula of area | The area of an Isosceles Trapezium is calculated by using the formula’ height x (sum of parallel sides ÷ 2)’. | The formula suggested for students to calculate the area of a Trapezium is ½ × (a + b) × h. |

**What is Isosceles Trapezium?**

An isosceles Trapezium is made of four edges, and two of them are parallel. The edges that are parallel have different measurements, while the other two edges have similar measures.

An isosceles Trapezium is a kind of Trapezium because it has all the properties a Trapezium has, yet it is considered to be very different.

The two adjacent angles of an isosceles Trapezium sum up to 180 degrees. Hence, a proper geometrical definition says that with two equal non-parallel sides and two equal angles, the shape formed is called Isosceles Trapezium.

The major specifications of an isosceles Trapezium are that it can be inscribed in a circle, and the diagonals of these shapes are congruent.

By congruent, a person can understand that the diagonals are equal. An interesting fact about a Trapezium is that the diagonals inscribed in it forms two pair of congruent triangles.

These triangles have a matching base, length, and height. If the exterior and interior angles of an Isosceles Trapezium are added up, then the sum would be four right angles.

A segment in Isosceles Trapezium joining the midpoint of parallel edges is usually perpendicular to them.

It is always suggested to draw a neat picture of isosceles Trapezium and write down the correct measurements of edges and diagonals for accurate results.

**What is Trapezium?**

A Trapezium is the part of a convex quadrilateral that has one pair of two opposite parallel sides. The other two opposite sides of a Trapezium are not equal. It is associated with Euclidean geometry.

The adjacent angles of a Trapezium add up to 180 degrees. Just like other geometrical shapes, the diagonals of the Trapezium intersect each other.

Just like isosceles and a square, the Trapezium can be inscribed in a circle. Trapezium has five types based on their unique qualities that are acute, obtuse, isosceles, right, and scalene Trapezium.

An acute Trapezium has two acute angles that are also adjacent. These angles are formed on the longer base edge of a Trapezium.

The obtuse Trapezium has interior angles that are greater than 90 degrees. Isosceles Trapezium are formed by two identical right Trapezium.

Right Trapezium is called by this name because they have a right angle (90 degrees). The last type of Trapezium is scalene Trapezium, and the main specification of this Trapezium is its uneven edges.

Trapezium has four edges, and each of them has different measurements. The definition of a Trapezium has always been a matter of conflict, and that’s why it has several meanings.

Even the number of types is not definite. Some days that a Trapezium has five types, while some accept three types of Trapezium.

**Main Differences Between Isosceles Trapezium and Trapezium**

- Isosceles Trapezium is the 2D shape that is utilized to figure out or measure the areas under the curve. On the other hand, Trapezium has no such utilization to offer.
- A real-life example of an Isosceles Trapezium can be a skate park ramp. On the other hand, real-life examples of a Trapezium can be tabletops and roofs on houses.
- Students use the formula’ height x (sum of parallel sides ÷ 2)’ to measure the area of an Isosceles Trapezium, while ‘½ × (a + b) × h’ is the formula to find the area of a Trapezium.
- Isosceles Trapezium is one of the type of the quadrilateral shape Trapezium. On the other hand, Trapezium is subcategorized into five distinct types.
- The parallel sides of an Isosceles Trapezium are not even. One of them is shorter than the other. On the other hand, Trapezium should have a pair of parallel sides regardless of their size.

**Conclusion**

In the architecture industry, shapes are the fundamental components to be understood. These shapes can be both two and three-dimensional.

Two-dimensional shapes don’t have a depth to be measured, while three-dimensional shapes have depth and volume.

Many shapes are subcategorized and have significant chapters solely dedicated to them. There are many aspects of a single shape that can bring a lot of changes.

For example, most of the buildings are either rectangular or square-shaped.

But how unique it would be if a building is in the shape of a Trapezium. The pyramids in Egypt are conical-shaped, while many beautiful buildings are cylindrical. Hence, each shape can bring unique and beautiful changes.

**References**

- https://nhess.copernicus.org/articles/9/1189/2009/
- https://www.sciencedirect.com/science/article/pii/S0363502381801657