LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

CLASSIFICATION OF TRIANGLE ON BASICS OF SIDES

__Classification of triangles on the
basics of sides –__

__Scalene
Triangle -__

**No two sides of a scalene triangle are equal. In the
figure, ABC is a scalene triangle as AB ≠ BC ≠ CA**

__Isosceles
Triangle –__

**An Isosceles triangle has two equal sides. In the figure, ABC is an isosceles triangle in
which AB = AC (equal sides are marked by an equal number of strokes). The third
side BC is called the base of the triangle, while ∠ABC and ∠ACB are called the base angles. ∠BAC is
called the vertical angle.**

**Property – **

**The angles opposite to the equal sides of an
isosceles triangle are equal.**

**In the figure, AB = AC,**

**So, ∠ABC = ∠ACB**

__Converse –__

**The converse, or opposite, of this is also true.
Thus, if two angles of a triangle are equal, the sides opposite to them are
equal.**

**In the figure, ∠ABC = ∠ACB.**

**So, AB = AC**

**
**

**This also implies that the angles of a scalene triangle are all unequal.**

__Equilateral Triangle
–__

**All the
three sides of an equilateral triangle are
equal. In the adjoining figure, ABC is an equilateral triangle as AB = BC = CA **

__Property
–__

**All the
angles of an equilateral triangle are equal.**

**In the
figure, ∠BAC = ∠ABC = ∠ACB**

__Converse –__

**If all the angles of a triangle are equal, it must be
an equilateral triangle.**

**In the adjoining figure, ∠P = ∠Q
= ∠R, **

**Hence, PQR is an equilateral
triangle.**