A triangle whose one of three angles is right angle, is called a right angled triangle.

Right angled triangle is a triangle and it is also formed by the three line segments but two of three line segments meet each other perpendicularly. Therefore, the angle between them is a right angle ($90^\circ$). Hence, the triangle is called as a right angled triangle.

The three sides of the right angled triangle are called by three special names but there is no significance for the sides of the other triangles.

1

The side which displayed in vertical direction is called opposite side. It is also called as perpendicular because it is perpendicular to the surface of the earth.

For example, $\overline{BC}$ is the opposite side of the right angled triangle $BAC$.

2

The side which displayed in horizontal direction is called adjacent side. It is also called as base because it is parallel to the surface of the earth.

For example, $\overline{AB}$ is the adjacent side of the right angled triangle $BAC$.

3

The side which displayed in slant and opposite to the right angle is called hypotenuse.

For example, $\overline{AC}$ is the hypotenuse of the right angled triangle $BAC$.

Three interior angles are formed in right angled triangle by the meeting of every two of three sides.

1

One of three interior angles is a right angle and it is the angle, formed by the meeting of opposite and adjacent sides.

For example, $\angle CBA$ (or) $\angle ABC$ (or) $\angle B = 90^\circ$

2

It is an interior angle which is an acute angle but it is the angle between hypotenuse and adjacent side. It is called as angle of the right angled triangle.

For example, $\angle BAC$ (or) $\angle CAB$ (or) $\angle A = \theta$.

3

It is also an interior angle and acute angle but it is the angle between opposite side and hypotenuse. There is no much importance to this angle.

For example, $\angle BCA$ (or) $\angle ACB$ (or) $\angle C$

A right angled triangle can be constructed geometrically by using geometric tools.

- Take ruler and draw a horizontal line of any length. In this example, $11$ centimetres line is drawn horizontally. The left and right side endpoints of line segments are called as point $D$ and $E$.
- Take protractor. Coincide centre of the protractor with point $D$ and then coincide right side base line with horizontal line $\overline{DE}$. After that identify $90^\circ$ angle by considering bottom scale and mark it.
- Take ruler and draw a straight line from point $D$ through $90^\circ$ angle line.
- Take compass and adjust it to have a particular distance (In this example $8$ Centimetres) between points of pencil lead and needle by considering the ruler. Draw an arc from point $D$ on $90^\circ$ angle line. The arc cuts the $90^\circ$ angle line at a particular point and call it as point $F$.
- Take ruler and join points $E$ and $F$.

The step by step geometrical procedure constructed a triangle, in which the points $D$, $E$ and $F$ are called as vertices. The line segments $\overline{DE}$, $\overline{EF}$ and $\overline{FD}$ are called sides.

1

The three sides are called by different names.

- The side $\overline{DF}$ is called opposite side and its length is $DF = 8$ Centimetres.
- The side $\overline{DE}$ is called adjacent side and its length is $DE = 11$ Centimetres.
- The side $\overline{EF}$ is called hypotenuse but its length ($EF$) is unknown. Take ruler and measure it. It will be $EF = 13.6$ centimeters exactly.

2

The triangle has three interior angles.

- The angle $\angle EDF$ (or) $\angle FDE$ (or) $\angle D$ is a right angle. It can be expressed as $\angle D = 90^\circ$.
- The angle $\angle DEF$ (or) $\angle FED$ (or) $\angle E$ is the angle of the right angled triangle but it is unknown. Measure the angle by using protractor. It will be $\angle E = 36^\circ$.
- The third interior angle $\angle DFE$ (or) $\angle EFD$ (or) $\angle F$ is unknown. So, measure it by using protractor and it will be $\angle F = 54^\circ$ exactly.

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