Page 169 - Maths Skills - 7

The Triangle and Its Properties 167

INTRODUCTION
Look at the triangles in Fig. below:

A triangle is a closed figure made of three line segments. It is the first polygon. A
In Fig. 1, AB, BC and CA form a closed figure. So, it is a triangle and is denoted as DABC. It
has six elements, the three sides AB, BC and CA and three angles ∠A, ∠B and ∠C.
The side opposite to vertex A is BC, side opposite to vertex B is AC. Can you name the side B C
opposite to vertex C? Fig. 1
Classification of triangle on the basis of:
(i) Sides: Scalene (all the sides are unequal), Isosceles (two sides are equal) and Equilateral (all the sides
are equal) triangles.
(ii) Angles: Acute-angled (each angle is acute), Obtuse-angled (only one angle is obtuse) and Right-angled
(only one angle is right angle) triangles.

INTERIOR AND EXTERIOR OF A TRIANGLE

Let us consider DABC in Fig. We see that all the points in the plane of DABC are divided into following
three parts.
1. The points which lie inside the region enclosed by DABC.
2. The points which lie on the sides, BC, CA and AB of DABC.

3. The points which lie outside the region enclosed by DABC.
Now, we define the following:
● Interior of Triangle: The part made up of points such as X which are enclosed by DABC is called the
interior of DABC. A
● Boundary of a triangle: A triangle ABC is the boundary of its interior. Q
● Exterior of a triangle: The part made up of points such as Y which are Y boundary
not enclosed by DABC is called the exterior of DABC. Exterior T X of D

● Triangular region: The interior of DABC together with its boundary is B Interior R
C
called the triangular region. S
Here, point X is in the interior. Points R, S, T are on its boundary. Points Y, Q, P
P are in the exterior of DABC. Fact-o-meter

MEDIANS OF A TRIANGLE � A median always lies in the interior

A line segment joining the vertex of a triangle.
of a triangle to the midpoint of Centroid � A triangle has three medians which
opposite side is called the median. always meet inside the triangle.
Three medians can be drawn in a � The point of intersection of three
triangle. In Fig.,.AD, BE and CF are medians of a triangle is called the
the three medians. centroid of the triangle.