Definition of a triangle
A triangle is a plane closed figure bounded by three line segments.
The components of a triangle are sides, vertices and angles.
Properties of triangles
The sum of the lengths of any two sides of a triangle, is always greater than the length of the third side.
Sum of the measures of the three angles of a triangle is always equal to 180°.
Types of triangles
Classification of triangles is done in two ways:
1. Based on the types of angles contained in the triangle
2. Based on the length of the sides of the triangle
Based on the types of angles in a triangle
Right angled triangle: A triangle with one right angle ( = 90° ) is called a right angled triangle.
Obtuse angled triangle: A triangle with one obtuse angle ( > 90° ) is called an obtuse angled triangle.
Acute angled triangle: A triangle with all three angles as acute ( < 90° ) is called an acute angled triangle.
Based on the length of the sides of a triangle
Equilateral triangle: A triangle whose all three sides are equal in length is called an equilateral triangle. In a equilateral triangle, each of the angles measure 60°.
Isosceles triangle: A triangle whose two sides are equal in length, is called an isosceles triangle. In an Isosceles triangle, the angles opposite to each other are equal.
Scalene triangle: A triangle whose all sides are of different length, is called a scalene triangle.
Question: In a right angled triangle, one of the acute angles measures 40°. Find the measure of the other acute angle.
( Answer: Sum of the measures of all the angles in a triangle = 180°
Hence 90° + 40° + x = 180°
X = 180° - 130°
X = 50°
Question: Which of the following cannot be the measures of the angles of a triangle?
1. Angle A = 50°, Angle B = 30°, Angle C = 100°
2. Angle A = 20°, Angle B = 50°, Angle C = 10°
3. Angle A = 70°, Angle B = 110°, Angle C = 20°
4. Angle A = 90°, Angle B = 45°, Angle C = 45°
5. Angle A = 50°, Angle B = 60°, Angle C = 70°
( Answer: 2, 3 )
Question: Triangle ABC is an equilateral triangle. What is the measure of each of the angles of triangle ABC?
( Answer: 60°, 60°, 60° )
© Hozefa Arsiwala and teacherlookup.com, 2016-2017. Unauthorized use and/or duplication of this material without express and written permission from this site’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Hozefa Arsiwala and teacherlookup.com with appropriate and specific direction to the original content.