explain tringales on the basis of …

Equilateral triangle: An equilateral triangle is a triangle whose all three sides are equal.

<a href="https://www.math-only-math.com/images/Equilateral-triangle.png" rel="gallery[pageGallery]" title="Equilateral Triangle"></a>

Here, XYZ is an equilateral triangle as XY = YZ = ZX.

Isosceles triangle: An isosceles triangle is a triangle whose any two sides are equal.

<a href="https://www.math-only-math.com/images/Isosceles-triangle.png" rel="gallery[pageGallery]" title="Isosceles Triangle"></a>

The adjoining figure shows an isosceles triangle where XY = XZ.

Scalene triangle: In a scalene triangle, all the three sides are unequal. 

<a href="https://www.math-only-math.com/images/Scalene-triangle.png" rel="gallery[pageGallery]" title="Scalene Triangle"></a>

The above figure shows a scalene triangle where XY ≠ YZ ≠ ZX.

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.

<a href="https://www.math-only-math.com/images/Acute-angled-triangle.png" rel="gallery[pageGallery]" title="Acute-angled Triangle"></a>

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.

<a href="https://www.math-only-math.com/images/Right-angled-triangle.png" rel="gallery[pageGallery]" title="Right-angled Triangle"></a>

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.

<a href="https://www.math-only-math.com/images/Obtuse-angled-triangle.png" rel="gallery[pageGallery]" title="Obtuse-angled Triangle"></a>

Here, ∠XYZ > 90°. 

Therefore, ∆ XYZ is an obtuse-angled triangle.