It gives information regarding triangles, their types & properties in mathematics. Helpful to school students.

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.