Question

Name the type of the triangle:
$\vartriangle PQR$ such that $PQ = QR = PR = 5cm$

Answer 1

Hint:
Here we need to determine the type of triangle. Triangle is a two-dimensional geometric figure which has three sides. There are different types of triangles based on the sides and the angles. Here we will use the properties of different types of triangles to find the required answer.

Complete step by step solution:
Here we need to determine the type of triangle.
It is given that $\vartriangle PQR$ and also it is given that $PQ = QR = PR = 5cm$.
We will draw the triangle using the given sides.

There are a total of six different types of triangles and they are equilateral triangle, isosceles triangle, scalene triangle, acute angles triangle, obtuse-angled triangle, and right-angled triangle.
As here only sides on the triangle are given and not angle so we will consider only equilateral triangle, isosceles triangle, and scalene triangle.
If only two sides or two angles of a triangle are equal then that type of triangle is known as the isosceles triangle. If all the sides and angles of the triangle are different than that type of triangle is known as the scalene triangle. However, if all sides of the triangle are equal then it is called an equilateral triangle.
We can see that all the sides of this triangle are equal.

Therefore, the given triangle i.e. $\vartriangle PQR$ is an equilateral triangle.

Note:
We can also identify the type of triangle based on the angle. We know that all the angles of an equilateral triangle are equal and it is equal to $60^\circ $. If two angles of a triangle are equal then it is called an isosceles triangle. If one of the angles of a triangle is equal to $90^\circ $ then it is called a right-angled triangle. When the angle of a triangle is less than $90^\circ $ it is called acute angle, whereas when the angle of a triangle is greater than $90^\circ $ it is called obtuse angle.