Isosceles Triangle, Equilateral Triangle, Scalene Triangle

Introduction

Isosceles triangle, equilateral triangle, and scalene triangle are the different types of triangles. A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180°, is constructed. It implies that a triangle's interior angles add up to 180°. It is the polygon with the fewest sides. To put it another way, a triangle is a three-sided, two-dimensional shape whose interior angles are 180°.

Types of Triangle

Triangles are primarily divided into six varieties based on the angles and side length. Let's go in-depth about the various triangle types.

The triangle is divided into three types according to the length of its sides −

• All of a triangle's sides in a scalene triangle have different side measurements.

• An isosceles triangle has two sides that are the same length.

• Triangles with equal side measures on each of their three sides are said to be equilateral triangles.

The triangles are further divided based on the angles into −

• Triangles with acute angles have all of their angles smaller than 90 degrees.

• Triangle with an obtuse angle has an angle that is larger than 90 degrees.

• Triangle with a right angle where one of the angles is 90 degrees

Scalene Triangles

All the sides of a scalene triangle are disjoint. Triangles with unequal sides are referred to as noncongruent triangles. For instance, a triangle would be referred to as a scalene triangle if its sides were 12, 30, and 23 cm. A scalene triangle cannot even have two sides that are the same. The scalene triangle's total angles are exactly 180 degrees, just like in all other triangles.

The Scalene Triangle: Facts.

• A scalene triangle has unique angles and sides.

• The smallest side is the one that faces the smallest angle.

• Its largest angle is direct across from its longest side.

• It cannot be split into two equal parts.

• It lacks a symmetry line.

• An acute scalene triangle, an obtuse scalene triangle, or a right scalene triangle are all examples of scalene triangles.

• Heron's formula can be used to determine the area of a scalene triangle if all the sides are known.

• Each angle in a scalene triangle that is inscribed in a circle is half the angle that the other side subtends.

• If all three angles are acute, the circumscribing circle's centre is located inside the triangle.

Isosceles Triangles

A triangle with two equal sides and one uneven side is said to be an isosceles. An isosceles triangle also has equal angles on either side of its equal sides. So, an isosceles triangle has two equal sides in addition to two equal angles. Legs and bases are the names for the equal and unequal sides, respectively. It is possible to divide an isosceles triangle into two identical right-angled triangles.

Information on the Isosceles Triangle

• The two angles that are opposite the equal sides are equal. The isosceles triangle base angle theorem states that the angles are therefore, also congruent.

• The angle that is not congruent with the two congruent base angles is known as the apex angle.

• An isosceles triangle's height, calculated from its apex, divides the base into two equal portions and the apex angle into two equal angles.

• An isosceles triangle can have an acute or obtuse third unequal angle.

• If all three angles of the three triangles are acute, the circumcentre of an isosceles triangle sits inside the triangle.

• In this case, the circumcentre is outside of the triangle since one of the angles is 90 degrees.

• The junction of the Isosceles triangle's medians is known as the centroid.

• The triangle is divided at right angles by the median obtained from the apex.

• An isosceles triangle's circumcentre is where the perpendicular bisectors of the triangle intersect.

• An isosceles triangle's angle bisectors come together at the incentre.

• Internally, the three sides of the triangle are touched by the circle that was drawn with the incentre.

• The isosceles triangle is split into two identical triangles with the same area by each median.

• When a circle is drawn with a diameter matching the base −

  • The apex of an isosceles triangle with an obtuse angle is located inside the circle.

  • The apex of a right-angled isosceles triangle is located on the perimeter.

  • The apex of an acute-angled isosceles triangle is outside the triangle's boundaries.

• When a circle is constructed with the midway of the base as the centre and the midpoint apex chosen as a radius

  • The base vertices of acute-angled isosceles are located inside the circle.

  • The base vertices for right-angled isosceles are located on the circumference.

  • The base vertices of an isosceles triangle with an obtuse angle are located outside the circle.

Equilateral Triangles

All three sides of an equilateral triangle are equal, and each interior angle is 60 degrees. Because all of the angles in an equilateral triangle are equal, it is also known as an equiangular triangle. Three scenarios allow for the estimation of an equilateral triangle's area −

• If one side and one angle's measurements are provided.

• When the triangle has three sides.

• If the triangle's two sides are known, as well as the angles they comprise.

Facts About Equilateral Triangle

• The sides of an equilateral triangle are all the same.

• The equilateral triangle has three identical angles.

• One line is shared by the median, altitude, angle bisector, and perpendicular bisector.

• The area of an equilateral triangle is Area = $\mathrm{\frac{\sqrt{3}}{4}\: side^2}$

• The same location is shared by the orthocentre, circumcentre, incentre, and centroid.

• The equilateral triangle's median is each altitude.

• The intersection of a triangle's angle bisectors, medians, and perpendicular bisectors is called the centroid.

Conclusion

In this tutorial, we learned about Triangles, types of triangles based on sides and their properties.

FAQs

1. List the several triangles that can be categorised depending on their sides.

A triangle can be divided into one of three sorts depending on its sides, namely −

Triangle of Scalene

Triangle of Isosceles

Triangle with equal sides

2. Give definitions for equilateral, isosceles, and scalene triangles.

The sides of a triangle in a scalene triangle are all of various lengths. Two of a triangle's sides have the same length in an isosceles triangle. All of a triangle's sides are the same length in an equilateral triangle.

3. A scalene triangle might be an acute triangle?

A scalene triangle, isosceles triangle, or equilateral triangle can all be classified as acute triangles. If the triangle's side lengths are equal or unequal, the acute triangle can be drawn.

4. What is the centroid of a triangle?

The centroid of a triangle is defined as the point where all three medians intersect each other.