CBSE Class 7 Mathematics Triangles and its Properties Notes Set 13

Parts and Kinds of Triangles

A triangle has three sides, three angles and three vertices. By sides it is equilateral (all equal), isosceles (two equal) or scalene (none equal). By angles it is acute (all less than 90°), right (one 90°) or obtuse (one more than 90°).
A median joins a vertex to the mid point of the opposite side; every triangle has three medians, all inside the triangle. An altitude is the perpendicular from a vertex to the opposite side; it may lie outside an obtuse triangle.

Angle Properties

The three angles of a triangle add up to 180°. An exterior angle, formed by extending a side, equals the sum of the two interior opposite angles and is greater than each of them. In an equilateral triangle each angle is 60°, and in an isosceles triangle the angles opposite the equal sides are equal.

Inequality of Sides

The sum of any two sides of a triangle is greater than the third, and the difference of any two sides is less than the third. So a third side of a triangle with sides a and b lies strictly between their difference and their sum.

Pythagoras Property

In a right triangle, the square on the hypotenuse equals the sum of the squares on the other two sides. Conversely, if the squares of two sides add up to the square of the third, the triangle is right angled. Triples such as 3, 4, 5 and 5, 12, 13 are examples.

Worked Example

The exterior angle at R of triangle PQR is 110° and angle Q = 50°. Since the exterior angle equals the sum of the interior opposite angles, angle P = 110° - 50° = 60°.