CAT Introduction to Triangles MCQ - Practice Questions & Answers

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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.