Triangles are one of the most used and one of the first shapes studied in geometry. Therefore, understanding the basic concepts, properties, type, angles, and every other detail is considered important by all the private math tutors and teachers around the globe. Interestingly, all types of triangles, such as the isosceles triangle or scalene, form out of straight-line segments with some angles and side length. Before discussing the isosceles triangles' properties, let us have a quick overview of the classification and angles of triangles.
A two-dimensional geometric shape made up of three-line segments connected at their endpoints or vertices is known as a triangle. They have three vertices, three sides, three angles and are classified into three types according to the lengths of their sides, such as:
All three sides are equal in length.
All three sides are unequal in length.
Its two sides are equal in length.
A triangle with all of its interior angles less than 900 is known as an acute angle triangle.
A triangle with one interior angle of more than 900 is an obtuse angle triangle.
A triangle with only one interior angle of 900 is known as a right-angle triangle.
A polygon with at least two sides of equal length, angles, three vertices, and three edges is an isosceles triangle. The sum of the internal angle of an isosceles triangle is always equal to 1800.
Like the isosceles triangles, other triangles also differ based on their side lengths and angles as they own individual properties. For example, scalene, isosceles and equilateral triangles are defined based on their sides. On the other hand, right angled triangles, acute angle triangles, and obtuse angle triangles are classified on the basis of their angles.
Below is the figure of an isosceles triangle. Take a look before we move to its properties.
Each triangle has basic properties that make it unique from others. Here are a few characteristics and properties of an isosceles triangle:
written as, P = 2a + b
You can also find the area of the isosceles triangle using the following formulas:
a = length of two equal sides
b = base of the isosceles triangle
h = height of the isosceles triangle
Numerous things around us and in the world are of isosceles triangle shape. Here are a few popular real-life examples of isosceles triangles:
As all triangles are of 180 degrees
Let x the vertex angle
And 2x+4 is the base angle
In mathematical form,
Vertex angle = x
Base angle = 2x + 4
Equation to find the vertex angle
⇒ x+(2x+4) + (2x+4) =180
⇒ 5x + 8 = 180
⇒ 5x = 172
⇒ x = 34.4
adding x value to find the base angle
⇒2x + 4
⇒2 (34.4) + 4
Hence, vertex angle = 34.4 and the base angle = 72.8
Perimeter of an isosceles triangle = P = 2a + b
a = 10 cm
b = 5 cm
putting values in formula
P = 2 (10) + 5
P = 20 + 5
P = 25
Hence, the perimeter of a given triangle is approximately 25 cm.
A = b/4[ √ (4a2 - b2)]
a = 5
b = 8
by putting values
A = 8/4 [ √ (4 (5)2 – (8)2)]
A = 2 [ √ (4 (5)2 – (8)2)]
A = 2 [ √ (4 (25) – (64))]
A = 2 [ √ (100 – 64)]
A = 2 [ √ 36]
A = 2 (6)
A = 12
Hence, the area of the given isosceles triangle is 12 units2
Fun Fact about Isosceles Triangles