Types of triangle and their Properties

Types of triangles in terms of sides

1. Scalene Triangle: Triangle having three unequal sides.
2. Isosceles Triangle: Triangle having two sides of equal length. 
3. Equilateral triangle: Triangle having three equal sides.

Types of triangle in terms of angles

1. Acute Angled Triangle: Triangle having three acute angles. 
2. Obtuse Angled Triangle: Triangle having one obtuse angle. 
3. Right Angled Triangle: Triangle having one right angle i.e $90{}^\circ $.

Points to remember

1. The sum of lengths of two sides of triangle is always greater than the third side.
AB + BC > AC ; AC + BC > AB; AB + AC > BC.

2. Angle Sum Property of a Triangle: The sum of measures of all three interior angles of a triangle is 180
$\angle A+\angle B+\angle C=180{}^\circ $

3. The angles opposite to equal sides of an isosceles triangle are also equal.
If AB = AC then $\angle B=\angle C$.

4. The sides opposite to equal angles of a triangle are also equal.
If $\angle B=\angle C$ then AB = AC.

5. An exterior angle of a triangle is equal to the sum of interior opposite angles.

6. Area of Triangle = $\frac{1}{2}\times base\times height$

7. Perimeter of Triangle = AB + BC + CA

8. Pythagoras Theorem: In a right angled triangle,   
$hypotenus{{e}^{2}}=bas{{e}^{2}}+perpendicula{{r}^{2}}$

9. If ABC is an equilateral triangle each of whose side is a units in length, then

Area of Triangle = $\frac{\sqrt{3}}{4}{{(Side)}^{2}}$

Height or Altitude(AD)= $\frac{\sqrt{3}}{2}(Side)$


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