Page 81 - Start Up Mathematics_6

Interior and exterior of an angle

An angle divides the region into three parts: its interior, its exterior
or on it.
The region constituted by the points which lie within the arms of R B
an angle is called its interior. Point P is in the interior of ∠AOB.
Since the two rays containing the angle extend indefinitely, therefore Q
interior of the angle also extends indefinitely. P
The region constituted by the points which lie outside the arms of
an angle is called its exterior. Point R is in the exterior of ∠AOB. O A
The point Q and the vertex O lies on the arms of the angle.

Example 10: Name the angles in the given figure. A

Solution: The angles in the given figure are
∠ABC, ∠BCA and ∠CAB.
Example 11: In the given diagram, name the point(s): B C
(a) In the interior of ∠DOE
(b) In the exterior of ∠EOF F H
(c) On ∠EOF C E
Solution: (a) Points A and G are in the interior of ∠DOE. B A

(b) Points C, A, G and D are in the exterior of ∠EOF. G
(c) Points E, B, O and F lie on ∠EOF. O D
A
Triangle
A three-sided polygon is called a triangle. In other words, a triangle Extension
is a closed figure formed by three line segments joining only at A triangle is a polygon
having least number
their end points. We write triangle ABC as ∆ ABC. B C of sides.
In ∆ ABC, the three sides are AB, BC and CA and the three angles are ∠ABC, ∠BCA and ∠CAB.
The three sides along with the three angles are called the parts or elements of the triangle. The
points A, B and C are called its vertices.

Interior and exterior of a triangle
In ∆ ABC, the region constituted by the points inside the triangle is C
called interior of the triangle. The region constituted by the points Exterior
outside the triangle is called exterior of the triangle and the points Interior
that lie on the triangle form the boundary of the triangle. The
boundary alongwith its interior is known as the triangular region. A B

Example 12: Draw a rough sketch of a triangle ABC. Mark points P and Q in its interior and a
point R in its exterior. Is point A in its exterior or in its interior? Is the line segment
joining PQ wholly contained in the interior of the triangle? C
Solution: Point A is neither in the interior nor in the exterior R Q
of the triangle. In fact it lies on the triangle. Line
segment PQ lies wholly in the interior of the triangle. P
A B

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