Right Triangle Labelled: Hypotenuse, Opposite and Adjacent

Grades 8-9

Question: Draw a right triangle and label it completely.

A right triangle is a special triangle in which one interior angle measures exactly

90^\circ

. This angle is usually denoted by the Greek letter

\gamma

and marked with a small square (the right-angle symbol).

Here are the key parts and labeling conventions for a right triangle:

Vertices: These are usually labeled counterclockwise with the capital letters $A$ , $B$ , and $C$ . In the standard layout, the right angle sits at vertex $C$ .
Sides: Sides are named with lowercase letters, matching the vertex opposite them.
- Hypotenuse ( $c$ ): The triangle's longest side. It lies directly opposite the right angle.
- Legs ( $a$ and $b$ ): The two shorter sides that form the right angle are called the legs. Relative to one of the acute angles (say $\alpha$ ), we further distinguish between the adjacent leg (next to the angle) and the opposite leg (across from the angle).
Angles: The interior angles at vertices $A$ and $B$ are labeled $\alpha$ and $\beta$ . Since every triangle's angles sum to $180^\circ$ and the right angle already takes up $90^\circ$ , $\alpha$ and $\beta$ must together also sum to $90^\circ$ ( $\alpha + \beta = 90^\circ$ ).

The diagram below shows such a triangle with all the standard labels, including the names for each type of side.