Math Doubts

Properties of Right triangle when angle equals to 0°

Properties

There are two fundamental properties between sides of a right triangle when its angle equals to zero degrees.

  1. Length of Opposite side (Perpendicular) = 0
  2. Length of Adjacent side (Base) = Length of Hypotenuse

Theorem

properties of right triangle whose angle equals to 0 degrees

$\Delta MON$ is a right triangle and it contains an angle of $0^°$. Assume, the length of adjacent side of this triangle is denoted by $d$.

Zero angle is possible geometrically in a right triangle when its length of opposite side is equal to zero.

$Length \, of \, Opposite \, side$ $\,=\,$ $0$

Due to zero length of opposite side, the length of hypotenuse is absolutely equal to length of hypotenuse. So, remember this property when angle of right triangle is zero.

$\,\,\, \therefore \,\,\,\,\,\,$ $Length \, of \, Adjacent \, side$ $\,=\,$ $Length \, of \, Hypotenuse$ $\,=\,$ $d$

Proof

A right triangle is required to construct with zero angle for proving its properties geometrically.

construction of right triangle whose angle equals to 0 degrees for its properties
  1. Draw a horizontal line from point $\small P$ in a plane.
  2. Identify zero angle from point $\small P$ and draw zero angle line from point $\small P$ but it appears on horizontal line.
  3. Set compass to a length (for example $7 \, cm$) by ruler. Now, draw an arc on zero angle line and they are intersected at point $\small Q$.
  4. It’s not possible to draw a perpendicular from $\small Q$ to horizontal line because horizontal and zero angle line are lie on same line. So, imagine a perpendicular line from $\small Q$ to horizontal line and it intersects the horizontal line at point $\small R$. In this way, a right angled ($\small \Delta RPQ$) is constructed in geometric system.

It is time to study the properties of right triangle ($\small \Delta RPQ$) when the angle of right angled triangle is zero degrees.

properties of right triangle whose angle equals to 0 degrees
  1. $\small \overline{QR}$ is opposite side or perpendicular. There is no distance between points $\small Q$ and $\small R$. So, the length of opposite side is zero.
  2. $\small \overline{PQ}$ is hypotenuse. It is $7 \, cm$ in this case.
  3. $\small \overline{PR}$ is adjacent side or base. Due to zero length of opposite side, the length of adjacent side is equal to length of hypotenuse exactly. So, the length of adjacent side $\small \overline{PR}$ is also $7 \, cm$.


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