Right Angled Triangle
A triangle having an angle `90^{0}` is called a right-angled triangle, whereas other (remaining) angles are acute angles (`90^{0}`). Three sides of the right-angled triangle are called Hypotenus (h), Perpendicular(p), and Base(b).
Area of right-angled triangle = `\frac{1}{2}` perpendicular (p) x base (b)
Perimeter of right-angled triangle = h + p + b
Reference Angle
As we know that the right-angled triangle has two acute angles, they are called reference angles which help us to identify its three sides (h,p,b).
In short, an acute angle, which is used to identify the hypotenuse, perpendicular, and the base is called a reference angle.
Hypotenuse
In any right-angled triangle, the side opposite to the right angle is called the hypotenuse. It is denoted by "h".
Please Note: Hypotenuse is the longest side.
Perpendicular
In any right-angled triangle side opposite to the reference angle is called perpendicular. It is denoted by "p".
Base
The remaining side of the right-angled triangle, having a right angle and reference angle is called base "b".
Pythagoras Theorem
Pythagoras theorem can be defined as follow:
"In any right-angled triangle, square made on the longest side (hypotenuse) is always equal to the sum of squares made on the remaining two sides (perpendicular and base)."
In short:
`h^(2)` = `p^(2)` + `b^(2)`
From which we can derive few more relations like this:
`p^(2)` = `h^(2)` - `b^(2)`
`b^(2)` = `h^(2)` - `p^(2)`
Exercise:
Q1 Define right-angled triangle.
Q2 Define hypotenuse, perpendicular and base with an example.
Q3 What is the formula to find the area and perimeter of a right-angled triangle?
Q4 Define Pythagoras Theorem.
Q4 Write down the relation of h, p and b on the basis of the Pythagoras theorem.
What have you learned?
- Right-angled triangle
- Its elements
- Name of its sides and its definitions
- The formula for the area and perimeter of a right-angled triangle
- Pythagoras theorem
- Relation of three sides of a right-angled triangle
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