AP Board Class 7 Maths Chapter 6 The Triangle and its Properties Complete Guide
A triangle has six elements: three sides and three angles. The medians join a vertex to the midpoint of the opposite side, while altitudes are perpendicular lines from a vertex to the opposite side.
The sum of a triangle's angles is always 180°, and any exterior angle equals the sum of its interior opposite angles.
The Pythagoras theorem applies only to right-angled triangles: the square of the hypotenuse equals the sum of the squares of the other two sides.
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AP Board Class 7 Mathematics Chapter 6 – THE TRIANGLE AND ITS PROPERTIES
Below are the key concepts will cover
1. The six elements of a triangle are its three angles and the three sides.
2. The line segment joining a vertex of a triangle to the mid point ofi ts opposite side is
called a median of the triangle. A triangle has 3 medians.
3. The perpendicular line segment from a vertex of a triangle to its opposite side is
called an altitude of the triangle. A triangle has 3 altitudes.
4. An exterior angle of a triangle is formed, when a side of a triangle is produced. At
each vertex, you have two ways of forming an exterior angle.
5. A property of exterior angles:
The measure of any exterior angle of a triangle is equal to the sum of the measures of its interior opposite angles.
6. The angle sum property of a triangle:
The total measure of the three angles of a triangle is 180°.
7. A triangle is said to be equilateral, if each one of its sides has the same length.
In an equilateral triangle, each angle has measure 60°.
8. A triangle is said to be isosceles, if at least any two of its sides are of same length.
The non-equal side of an isosceles triangle is called its base; the base angles of an isosceles triangle have equal measure.
9. Property of the lengths of sides of a triangle:
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
The difference between the lengths of any two sides is smaller than the length of the third side.
This property is useful to know if it is possible to draw a triangle when the lengths of the three sides are known.
10. In a right angled triangle, the side opposite to the right angle is called the hypotenuse and the other two sides are called its legs.
12. Pythagoras property:
Ina right-angled triangle, the square on the hypotenuse = the sum of the squares on its legs.
If a triangle is not right-angled, this property does not hold good. This property is useful to decide whether a given triangle is right-angled or not.
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