Page 131 - classs 6 a_Neat

In the figure given above, ∆ ABC is an equilateral triangle in which AB = BC = CA.

8 Triangle (ii) ISOSCELES TRIANGLE A triangle having two sides equal ts called an isosceles triangle.

Triangle Let A, B and C be three non collinear points

Then, the figure formed by the three line segments AB, BC and CA
is called a triangle with vertices A, Band C.
Such a triangle is denoted by the symbol .∆ABC.

A. ∆ABC has: In the above figure, ∆DEF is an isosceles triangle in which DE = DF.
(i) three sides, namely, AB, BC and CA;
(ii) three angles, namely, BAC, ABC and BCA to be denoted by A, B and C respectively. (iii) SCALENE TRIANGLE A triangle having three sides of different lengths is called a scalene triangle.

The three sides and three angles of a triangle are together called the six parts or six elements of the triangle.

In .∆ABC, the points A, Band Care called its vertices.
Clearly, A is the vertex opposite to the side BC.
Similarly, Bis the vertex opposite to the side CA.
And, C is the vertex opposite to the side AB. In the above figu re, ∆ PQR is a scalene triangle, as PQ ≠ PR ≠ QR.

CONGRUENT TRIANGLES Two triangles are said to be congruent PERIMETER OF A TRIANGLE The sum of the lengths of the sides of a triangle is called its perimeter.
if every angle of one ts equal to the corresponding angle of the other
and every side of one ts equal to the corresponding side of the other. NAMING TRIANGLES BY CONSIDERING THEIR ANGLES

0
∆ABC and ∆DEF are congruent triangles because (i) ACUTE TRIANGLE A triangle each of whose angles measures less than 90 is called an acute-angled trian-
A = D, B= E, C= F,AB =DE,BC= EF and CA= FD. gle or simply an acute triangle.

INTERIOR AND EXTERIOR OF A TRIANGLE

(i) The part of the plane enclosed by ∆ABC is called the interior of ∆ABC.
∆ABC ts the boundary of its interior.
(ii) The part of the plane not enclosed by
∆ABC is called the exterior of ∆ABC.

In the adjoining figure P, Q, R are the interior points of
∆ ABC. E and F are the exterior points of ∆ABC.
And, D lies on ∆ABC.
In the above figure, each angle of ∆ABC is an acute angle. So, ∆ABC is an acute triangle.
REMARK if p and Q are two interior points of .6 ABC then the line segment PQ lies entirely in the
0
interior of ∆ABC. (ii) RIGHT TRIANGLE A triangle whose one angle measures 90 is called a right-angled triangle or simply a
right triangle.
VARIOUS TYPES OF TRIANGLES

NAMING TRIANGLES BY CONSIDERING THE LENGTHS OF THEIR SIDES

(i) EQUILATERAL TRIANGLE A triangle having all sides equal
is called an equilateral triangle.