[Maths Class Notes] on Isosceles Triangle Equilateral Pdf for Exam

Triangles Equilateral

A triangle consists of 3 sides and 3 angles. The 3 angles of a triangle always add to 180°, regardless of the measure of any of the angles. There are basically 3 types of triangles and each triangular shape is classified based on the length of its sides or the measure of their angles. These classifications of three’s based on the sides involve:

1. Isosceles Triangle: 

A triangle with a minimum of sides congruent

2. Equilateral Triangle: 

A triangle with at least or say all 3 sides congruent

3. Scalene Triangle: 

A triangle with absolutely no sides congruent

An Equilateral Triangle Is An Isosceles Triangle?

Isosceles triangle and equilateral triangle share a peculiar relation. An equilateral triangle is that triangle that has 3 equal sides. However, an isosceles triangle is one with only 2 equal sides.

Thus, every equilateral triangle is or can be isosceles, but not every isosceles triangle is equilateral.

How to Identify an Equilateral Triangle?

An equilateral triangle is that whose all sides are equal. It is a particular type of an isosceles triangle whose base is equivalent to each leg, and whose vertex angle is equivalent to its base angles.

Besides the sides of an equilateral triangle, all the three angles of an equilateral triangle are also equal. This holds true because of a unique property of isosceles equilateral triangles. 

This is to say that every equilateral triangle is also an isosceles triangle, so any 2 sides that are in congruence to one another will also have equal opposite angles. Thus, seeing that all 3 sides of an equilateral triangle are equal, all 3 angles are equal, too. Therefore, every equilateral triangle also makes for an equiangular.

Identifying Equilateral Triangles

As already explained above, an equilateral triangle contains 3 equal sides and 3 equal angles (60° each). Its equal angles not only make it equiangular but equilateral too. You might not often hear the term equiangular triangle, but, since the only triangle that’s equiangular is the equilateral triangle, and that everyone calls this triangle equilateral. 

That being said, you need to consider both terms in case of quadrilaterals and other polygons. This is because an equiangular geometric figure, like a rectangle, can contain sides of different lengths, and an equilateral figure, like a rhombus, can contain angles of different measures.

How to Identify the Scalene Triangle?

Besides, having 3 unequal sides, scalene triangles consist of 3 unequal angles as well. In addition, below are the few properties that will help you better in determining scalene triangles:

• The shortest side is to the other side from the smallest angle

• The medium side is to the other side from the medium angle,

• The longest side is to the other side from the largest angle.

• The ratio of sides is not equal to the ratio of angles.

• It would be wrong to assume that if one side of a scalene triangle is, say, two times in length as the other side than the angles opposite those sides are also in a ratio of 2 : 1.

• The ratio of the sides may be close to the ratio of the angles, but the ratios are never exactly equal (other than when the sides are equal).

Type of Angle to Determine a Triangle

Triangles can have names that tell us about what kind of angle is inside:

For example:

• In an Acute Triangle, all angles are less than 90°

• In a Right Triangle, one angle is (90°)

• In an Obtuse Triangle, one angle is more than 90°