There are three fundamental properties between sides of a right triangle when its angle equals to $90$ degrees.
$\Delta QPR$ is a triangle, which represents a right triangle with $90^°$ angle.
It is possible to construct a right triangle with $90^°$ angle only when the length of adjacent side (base) is zero.
$Length \, of \, Adjacent \, side$ $\,=\,$ $0$
$\implies PR \,=\, 0$
When length of adjacent side ($\overline{PR}$) is zero, the lengths of opposite side (perpendicular) and hypotenuse are equal.
In this example, the length of opposite side is represented by $d$.
$\,\,\, \therefore \,\,\,\,\,\,$ $Length \, of \, Opposite \, side$ $\,=\,$ $Length \, of \, Hypotenuse$ $\,=\,$ $d$
$\implies QR = PQ = d$
Now, let’s talk about the angles of this triangle.
The length of adjacent side becomes zero because the $\angle PQR$ becomes zero angle. Therefore $\angle PQR = 0^°$. Whenever the $\angle PQR$ becomes zero, the angles $\angle RPQ$ and $\angle QRP$ become right angles.
$\angle RPQ$ $\,=\,$ $\angle QRP$ $\,=\,$ $90^°$
The properties of right triangle when its angle equals to $\dfrac{π}{2}$, can be proved geometrically by constructing a right triangle with $90$ degrees angle.
A right triangle, represented by $\Delta NLM$ is formed geometrically. Finally, it is your time to study the properties of right triangle when its angle is a right angle.
$\overline{LN}$ is adjacent side and its length is zero because there is no distance between the points $L$ and $N$.
$LN \,=\, 0$
$\overline{MN}$ represents opposite side and $\overline{LM}$ represents hypotenuse but the points $L$ and $N$ are at same position. Therefore, the lengths of opposite side and hypotenuse are equal if the angle of right triangle is $90^°$. In $\Delta NLM$, the length of hypotenuse is $8 \, cm$. Hence, the length of opposite side is also equal to $8 \, cm$.
$LM \,=\, MN \,=\, 8$
Due to zero length of adjacent side, the $\angle LMN = 0^°$. The $\angle MLN$ and $\angle MNL$ are right angles. Therefore, $\angle MLN = \angle MNL = 90^°$
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