Here we will discuss about classification of triangles on the basis of their sides and angles
Equilateral triangle: An equilateral triangle is a triangle whose all three sides are equal.
Here, XYZ is an equilateral triangle as XY = YZ = ZX.
Isosceles triangle: An isosceles triangle is a triangle whose any two sides are equal.
The adjoining figure shows an isosceles triangle where XY = XZ.
Scalene triangle: In a scalene triangle, all the three sides are unequal.
The above figure shows a scalene triangle where XY ≠ YZ ≠ ZX.
Classification of Triangles on the Basis of Their Angles
Acute-angled triangle: If all the three angles of a triangle are acute angles (i.e., each measures less than 90°), it is called an acute-angled triangle.
Here, ∠XYZ, ∠YZX and ∠ZXY are all acute angles.
Right-angled triangle: If one of the angles of a triangle is a right angle (i.e., measures 90°), it is called a right-angled triangle.
Here, <XYZ = 90°.
Therefore, ∆ XYZ is a right-angled triangle.
Obtuse-angled triangle: If any of the three angles of a triangle is an obtuse angles (i.e., measures more than 90°), it is called an obtuse-angled triangle.
Here, ∠XYZ > 90°.
Therefore, ∆ XYZ is an obtuse-angled triangle.
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