Triangle || Part 04 || Right Angle Triangle And Its Properties

Right Angle Triangle And Its Properties

Triangle:- A polygon with three edges, three vertices and three angles is called Triangles. A triangle with vertices A, B, and C is denoted by ∆ABC.

Right Triangle or Right Angle Triangle

A triangle whose one interior angles is right angle (90°) is called Right Triangle or Right Angle Triangle.  

1. Isosceles Right Triangle: 

A Right Angle Triangle with two equal sides is called an isosceles right triangle.

2. Right Scalene Triangle: 

A Right Angle Triangle with unequal sides is called an acute Scalene triangle.

Properties of a Right Angle Triangle

*1) A right angle triangle has a right angle and the other two angles of a right-angle triangle are acute angles.

*2) The side opposite to the right angle is the largest side of the triangle and it is specially named as hypotenuse.

Name Of The Sides Of The Right Angle Triangle

1. Hypotenuse :- Side opposite to right angle is called Hypotenuse. 

We also used this name for opposite side of a given angle. 

2. Base :- Horizontal side of a triangle is known as base. 

Base is the adjacent side of a given angle.

3. Perpendicular :- Non-horizontal side of a triangle is known as Perpendicular. 

Perpendicular is the other adjacent side of a given angle.

Relationship Between The Sides Of The Triangle

Right-Angle Triangle

Pythagoras Theorem

"The square of the hypotenuse (Largest side) is equal to the sum of squares of the other two sides“. This is known as Pythagoras Theorem.

In the ∆ACB :

(AC)² + (BC)² = (AB)²

Special cases of Right Angle Triangles

In 45°-45°-90° Triangle

In this triangle,

First angle is a right angle and the other two angles measure 45° & 45°. This is also called an right isosceles triangle. 

The angles of this triangle are in the ratio – 1: 1: 2, Then sides of this triangle will be in the ratio – 

B : P : H = 1: 1: √2 respectively.

In 30°-60°-90° Triangle

In this triangle,

First angle is a right angle (90°) and the other two angles measure 30° & 60°.

This is also called an right Scalene triangle. 

The angles of this triangle are in the ratio – 1: 2: 3, Then sides of this triangle will be in the ratio – 

B : P : H = 1: √3: 2 respectively.

Pythagorean Triplets

A triple of positive integers (a, b, c) which satisfy the equation a² + b² = c² is called a Pythagorean triple. if a, b, c have no common factor, Such a triple is called primitive triple.

(3, 4, 5), (5, 12, 13), (6, 8, 10), (8, 15, 17), (7, 24, 25), (9, 40, 41), (11, 60, 61)

The formula for Area of Triangle 

Area of any triangle   = ½ × Base × Height