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CAT Introduction to Triangles - Practice Questions & MCQ

Edited By admin | Updated on Oct 04, 2023 04:20 PM | #CAT

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In equilateral triangle, each angle measures 

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Introduction to Triangles

You have studied about triangles and their various properties in your earlier classes. You know that a closed figure formed by three intersecting lines is called a triangle. (‘Tri’ means ‘three’). A triangle has three sides, three angles and three vertices. For example, in triangle ABC, denoted as ∆ ABC; AB, BC, CA are the three sides, ∠ A, ∠ B, ∠ C are the three angles and A, B, C are three vertices.

Types of Triangle

Equilateral Triangle: A triangle having all sides equal is called an equilateral triangle.

Here, ABC is a triangle in which AB = BC = CA \therefore \triangle A B C is an equilateral triangle.

Isosceles Trianle: A triangle having two sides equal is called an isosceles triangle.

Here, ABC is a triangle in which AB = AC \therefore \triangle A B C is an isosceles triangle.

Scalene Triangle: A triangle in which all the sides are of different lengths is called a scalene triangle.

Here, ABC is a triangle in which AB \neq BC \neq CA \therefore \triangle A B C is a scalene triangle.

Acute-angled triangle: A triangle in which every angle measures more than 0^{\circ} but less than 90^{\circ} is called an acute-angled triangle.

Here, ABC is a triangle in which every angle is an acute angle. \therefore \triangle A B C is an acute-angled triangle.

Right Angled Triangle: A triangle in which one of the angles measures 90^{\circ} is called a right-angled triangle or simply a right triangle. In a right-angled triangle, the side opposite to the right angle is called its hypotenuse and the remaining two sides are called its legs.

In the given figure, \triangle A B C is a right triangle in which \angle B=90^{\circ}, AC is the hypotenuse, and AB, BC are its legs.

Obtuse-angled triangle: A triangle in which one of the angles measures more than 90^{\circ} but less than 180^{\circ} is called an obtuse-angled triangle.

Here, ABC is a triangle in which \angle ABC is an obtuse angle. \therefore \triangle ABC is an obtuse-angled triangle.

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