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VARIOUS TYPES OF TRIANGLES

NAMING TRIANGLES BY CONSIDERING THE LENGTHS OF THEIR SIDES (ii) RIGHT TRIANGLE A triangle whose one angle measures 900 is called a right-angled triangle or simply a
right triangle.
(i) EQUILATERAL TRIANGLE A triangle having all sides equal ts called an equilateral triangle L

A

900
M Right Triangle N
B C
Equilateral triangle In the above figure, ∆LMN is a right triangle, as LMN = 900•

In the figure given above, ∆ABC is an equilateral triangle in which AB = BC = CA.
(iii) OBTUSE TRIANGLE A triangle one of whose angles measures more than 900 ls called an obtuse-angled
(ii) ISOSCELES TRIANGLE A triangle having two sides equal ts called an isosceles triangle triangle or simply an obtuse triangle. R
D

1200
P Obtuse Triangle Q

In the above figure, ∆PQR is obtuse. So, ∆PQR is an obtuse triangle.
E F
Isosceles triangle
SOME IMPORTANT RESULTS
In the above figure, ∆DEF is an isosceles triangle in which DE = DF.
RESULT 1. Each angle of an equilateral triangle measures 60°.
(iii) SCALENE TRIANGLE A triangle having three sides of different lengths is called a scalene triangle. RESULT 2. The angles opposite to equal sides of an isosceles triangle are equal.
RESULT 3. A scalene triangle has no two angles equal.
P

ANGLE SUM PROPERTY OF A TRIANGLE

The sum of the angles of a triangle is 180°, or 2 right angles.
Q R As a consequence of the above result, we can say that
Scalene triangle

In the above figu re, ∆ PQR is a scalene triangle, as PQ ≠ PR ≠ QR. (i) a triangle cannot have more than one right angle,
(ii) a triangle cannot have more than one obtuse angle,
PERIMETER OF A TRIANGLE The sum of the lengths of the sides of a triangle is called its perimeter. (iii) in a right triangle, the sum of the two acute angles is 900•

NAMING TRIANGLES BY CONSIDERING THEIR ANGLES ILLUSTRATIVE EXAMPLES

(i) ACUTE TRIANGLE A triangle each of whose angles measures less than 900 is called an acute-angled EXAMPLE 4: find the angles of a triangle which are in the ratio 2 : 3: 4.
triangle or simply an acute triangle. A
550 SOLUTION: Let the measures of the given angles be (2x)0, (3x)0 and (4x)0
=>
Then 2x + 3x + 4x = 4x = 180 9x = 180 x = 20.
=>
Hence, the measures of the angles of the given triangle are 40°, 60° and 80°
650 600
B C
Acute Triangle
In the above figure, each angle of ∆ABC is an acute angle. So, ∆ABC is an acute triangle.