**Important Concepts and Formulas**

1. A triangle has six elements—three
angles and three sides.

2. A median of a triangle is a line
segment joining one vertex and the mid-point of the opposite side. A triangle
has three medians.

3. An altitude of a triangle is the
perpendicular line segment drawn from one vertex to the opposite side. A
triangle has three altitudes.

4. Exterior angles are formed when the
sides of a triangle are extended. A triangle has three exterior angles.

5. Triangles can be classified on the
basis of sides and angles.

·
On
the basis of sides:

I.
An
equilateral triangle has all sides equal.

II.
An
isosceles triangle has two of its sides equal.

III.
A
scalene triangle has all sides unequal

·
On
the basis of angles:

I.
In
a triangle, if all the angles measure less than 90Âº, then it is an acute-angled
triangle.

II.
In
a triangle, if one of the angles measures more than 90Âº, then it is an
obtuse-angled triangle.

III.
In
a triangle, if one of the angles measures 90Âº, then it is right-angled triangle.

6. The sum of measures of the three
angles of a triangle is 180°. This is called angle sum property.

7. An exterior angle is always equal to
the sum of two interior opposite angles. This is called exterior angleproperty.

8. According to Pythagoras theorem, in a
right-angled triangle, the square of the hypotenuse is equal to the sum of the
squares of the two legs. (Hypotenuse)

^{2}= (Base)^{2}+ (Height)^{2}