A triangle is defined as a closed figure made up of three line segments and has key properties such as vertices, base, altitude, median, centroid, perimeter, and angles. Triangles can be classified based on their angles (acute, obtuse, right) and their sides (equilateral, isosceles, scalene). Important properties include the angle-sum property (sum of angles equals 180 degrees) and the exterior angle property (an exterior angle is equal to the sum of its interior opposite angles).

1. TRIANGLES & ITS
PROPERTIES
RISHIKA SINGH
7th C
18

2. Definition of a triangle-
• A triangle is a closed figure made up of three line
segments.

3. Triangle properties-
 Vertex: Vertex is a corner of the triangle. Every
triangle has three vertices.
 Base: The base of a triangle can be anyone of the
three sides, usually the one drawn at the bottom.
 Altitude: The altitude of a triangle is the
perpendicular from the base to the opposite vertex.
 Median: The median of a triangle is a line from a
vertex to the midpoint of the opposite side.

4.  Centroid: The three medians intersect at a single
point, called the centroid of the triangle.
 Perimeter: The sum of all three sides of a triangle.
 Interior angles: The three angles on the inside of the
triangle at each vertex.
 Exterior angles: The angle between a side of a
triangle and the extension of an adjacent side.

5. Types of triangles based on angles-
• Acute-angled triangle: A triangle whose all angles
are acute.

6. • Obtuse-angled triangle: A triangle whose one angle is
obtuse.

7. • Right-angled triangle: A triangle whose one angle is a
right angle.

8. Types of triangles based on sides:
• Equilateral triangle: A triangle having all three sides
of equal length.

9. • Isoceles triangle: A triangle having two sides of
equal length.

10. • Scalene triangle: A triangle having three sides of
different lengths.

11. Basic properties of a triangle-
 Sum of the angles in a triangle is 180 degree. This is
called the angle-sum property.
 Sum of the lengths of any two sides of a triangle is
greater than the length of the third side.
 The side opposite to the largest angle is the longest
side of the triangle & the side opposite to the smallest
angle is the shortest side of the triangle.

12. In fig. above, angle B is the largest angle & the side
opposite to it is the largest side of the triangle.
• An exterior angle of a triangle is equal to the sum of
its interior opposite angles. This is called the exterior
angle property of a triangle.

13. ∠ACD is the exterior angle to the ∆ABC.
According to the exterior angle property,
∠ACD = ∠CAB + ∠ABC.