A significant segment of mathematics known as geometry is based on studying different shapes. These shapes are everywhere, but people barely notice them.
Geometry elaborates on these shapes and introduces students to the formulas and techniques to understand them. Isosceles Trapezium and Trapezium are two conditions that might look alike but are very different.
Key Takeaways
- An isosceles trapezium is a specific type with congruent non-parallel sides, while a trapezium is a general term for a quadrilateral with one pair of parallel sides.
- Isosceles trapeziums have additional geometric properties, such as equal base angles and symmetry, compared to general trapeziums.
- Both isosceles trapeziums and trapeziums belong to the family of quadrilaterals, but isosceles trapeziums have specific characteristics that distinguish them from other types of trapeziums.
Isosceles Trapezium vs Trapezium
A trapezium is a quadrilateral with at least one pair of parallel sides. The non-parallel sides are called the legs, and the parallel sides are called the bases. An isosceles trapezium is a particular case of a trapezium in which the legs are equal length. As a result, the two non-parallel sides of an isosceles trapezium are also of similar size.
Isosceles Trapezium, or 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 Trapeziums. It is one quadrilateral with four vertices and four edges.
Isosceles Trapezium also has an area and perimeter to be measured.
Trapezium, or Trapezoid, is another two-dimensional shape studied in geometry. It is a type of quadrilateral because it has four vertices and four edges.
The trapezium is divided into five classes: scalene, Isosceles, obtuse, acute, and right. It has a pair of parallel lines and the properties of a convex polygon.
Comparison Table
| 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 | A Trapezium is one of the most irregular quadrilateral shapes associated with fields. | An isosceles Trapezium is made of two identical Trapeziums that can be observed by a bisector in between. |
| Features | ‘ An Isosceles Trapezium’s area is calculated using the formula’ height x (sum of parallel sides ÷ 2)’. ‘ An IsTrapezium’spezium’s area is calculated usformula’formula’ height x (sum of parallel sides ÷ 2)’. | ” An Isosceles Trapezium’s area is calculated using the formula’ height x (sum of parallel sides ÷ 2)’. ‘ An Isosceles Trapezium’s area is calculated using the formula’ height x (sum of parallel sides ÷ 2)’. ” An Isosceles Trapezium’s area is calculated using the formula’ height x (sum of parallel sides ÷ 2)’. ‘ An Isosceles Trapezium’s area is calculated using the formula’ height x (sum of parallel sides ÷ 2)’. |
| Formula of area | An Isosceles Trapezium’s area is calculated using the formula’formula’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 parallel edges have different measurements, while the other two advantages 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 congruence, a person can understand that the diagonals are equal. An interesting fact about a Trapezium is that the diagonals inscribed form two 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 the Isosceles Trapezium joining the midpoint of parallel edges is perpendicular to them.
It is always suggested to draw a neat picture of the isosceles Trapezium and write down the correct measurements of edges and diagonals for accurate results.
What is Trapezium?
A Trapezium is part of a convex quadrilateral with 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. Like other geometrical shapes, the diagonals of the Trapezium intersect each other.
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 sharp 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. Two identical right Trapezium forms Isosceles Trapezium.
This name calls the right Trapezium 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, a Trapezium has five types, while others accept three kinds of Trapezium.
Main Differences Between Isosceles Trapezium and Trapezium
- Isosceles Trapezium is the 2D shape used 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. ‘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 types 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.
- https://nhess.copernicus.org/articles/9/1189/2009/
- https://www.sciencedirect.com/science/article/pii/S0363502381801657
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